When should a supervisor be a co-author? What are people's views on this?  To be specific: suppose a PhD student has produced a piece of original mathematical research. Suppose that student's supervisor suggested the problem, and gave a few helpful comments, but otherwise did not contribute to the work.  Should that supervisor still be named as a co-author, or would an acknowledgment suffice?
I am interested in two aspects of this. Firstly the moral/etiquette aspect: do you consider it bad form for a student not to name their supervisor?  Or does it depend on that supervisor's input?  And secondly, the practical, career-advancing aspect: which is better, for a student to have a well-known name on his or her paper (and hence more chance of it being noticed/published), or to have a sole-authored piece of work under their belt to hopefully increase their chances of being offered a good post-doc position?
[To clarify: original question asked by MrB ]
 A: In my situation (in Iran), it is obligatory for a PhD student to publish one or two papers to  graduate. Thus, I have a personal and strict rule: I won't be a co-author since I'm getting paid to help my PhD student to graduate. For that reason, I am not looking for any other excuses and/or reasonss (e.g. weakness of student, my substantial work, and so on) to be a co-author. To put it simply, that is my job to help! Obviously, I try to do my job well! 
I'd like to ask a related question that I think as a separate MO question has a great chance to get closed: Do you know any other country (or institution) with such obligation for PhD students?
A: First of all, this question must be decided by the adviser, not by the student.
The student must accept any decision if his/her adviser.
Most advisers that I know (mathematicians) will not co-author a paper with a student, if
the contribution of a student is substantial. But this depends on a person of course,
in particular on the adviser's own experience when s/he was a student.
For example, the first paper of Ahlfors was not written by himself (though the main idea was his). As a result, Ahlfors established a rule to never co-author his PhD student paper.
(He mentions this is his comments to his first paper in his Collected papers).
Myself, I try to follow this rule, but exceptions are possible.
A: This thread should be community wiki.
The AMS has adopted ethical guidelines regarding co-authorship; see
http://www.ams.org/about-us/governance/policy-statements/sec-ethics
The most relevant paragraph says
"A claim of independence may not be based on ignorance of widely disseminated results. On appropriate occasions, it may be desirable to offer or accept joint authorship when independent researchers find that they have produced identical results. All the authors listed for a paper, however, must have made a significant contribution to its content, and all who have made such a contribution must be offered the opportunity to be listed as an author. Because the free exchange of ideas necessary to promote research is possible only when every individual's contribution is properly recognized, the Society will not knowingly publish anything that violates this principle, and it will seek to expose egregious violations anywhere in the mathematical community."
The questions remain: when has an advisor made a "significant contribution" to the contents of the paper, and when should an advisor agree to be an author on the paper? My rule of thumb is that if I suggest a problem and react to discussions with a student by giving suggestions and helping with background and helping with proofs, then I will not be a co-author.  If I do work by myself on the paper, doing important technical work, then I must be a co-author.  There is of course a large gray area...
The tradition of advisors as co-authors differs a lot by discipline.  In experimental sciences, the advisor is essentially always a co-author.  I think that Angelo and I reflect common practice in pure mathematics, while the practice in applied mathematics is between that in pure mathematics and the experimental sciences.
A: "When should a supervisor be a co-author?"  One situation is when the paper wouldn't get published otherwise.  For example, yesterday (literally) I submitted for publication a paper that I coauthored a paper with my Ph.D. student, which we contributed to equally.   I asked him a few months ago if he was going to publish this section of his thesis, and he said he wasn't since he was too busy with his current job as a software engineer at Google (he left academia).  I then suggested that we coauthor the paper, and I would do all the (substantial) work of getting it into shape for publication.   
A: My suggested rule is: 
1) A supervisor should be a co-author in a paper taken from a student's thesis if she has contributed substantially to the research
2) A supervisor should not be a co-author in a paper taken from a student's thesis if she has not contributed substantially to the research
There are different styles of supervisions among different people. (And also for the same supervisor in case of different students.) A style where the supervisor and the student conduct joint research is certainly legitimate and it has various advantages. In such a case it is more likely that there will be a joint paper written. (But also in such cases, if the supervisor's contribution to the actual research is not substantial then the supervisor should not be a coauthor.) 
A: As a non-mathematician, I am somewhat mystified by the prevailing norms of the mathematics community as I understand them from this thread. Correct me if I'm wrong, but it sounds like: 


*

*Supervisors make important intellectual contributions to the thesis work of their students. 

*Typically, the name of the supervisor does not appear on the work. 
For example, the most upvoted comment at the moment says "as a rule the supervisor should not be a co-author in the main paper taken from a student's thesis, even if he has contributed substantially to it." (emphasis is mine) Other comments echo the sentiment. 
This seems problematic, both morally and practically. In other scientific communities, the author list is supposed to reflect the people who contributed intellectually to the paper. Manipulating it is an ethical offense. For example, the practices described in this thread appear to violate IEEE policies on authorship which state (Section 8.2.1)

Authorship and co-authorship should be
  based on a substantial  intellectual
  contribution ... the
  list of authors on an article serves
  multiple purposes; it  indicates who
  is responsible for the work and to
  whom questions  regarding the work
  should be addressed.

Finally, I would just like to add that as a student, I would feel horrible submitting a paper authored only by me if the paper was based in large part on the insights of someone else.  
A: I think that we should apply the same common sense rules as for any other collaboration (essential contribution - yes; inessential - no). 
However, the question is whether a supervisor should contribute substantially to a thesis. I think that normally they should not. Again, there is a bit of a grey area here.
A: I actually wouldn't worry too much about coauthorship affecting a student's chances at a postdoc.  For that, the advisor should just write in their letter that it's really all the student's work; I would say people don't tend to pay a lot of attention to whether graduating students even have publications, unless there are many of them or they are in very good journals.  What matters is what the letters say about the person's research.
Where I have seen this hurt job candidates severely is if they are still coauthoring all their papers with their advisor a couple of years after they graduate and are applying for tenure-track positions.  I think people see that and they wonder if the candidate is ever going to be independent.
A: I guess my viewpoint is rather parochial, but when I saw the question, I wondered where OP got such ideas of politeness. Reading the previous answers, though, I realized that different practices may be current, depending on the national culture, or even the culture of the university in question. Speaking strictly for myself, I would have considered it quite improper to have my name on a student's thesis, in effect robbing the student of the credit that was deserved.
A: I fail to see the difference between a supervisor and anyone else. To decide whether a supervisor should be a co-author, you should apply the same rules you would have applied in any other case.
I generally prefer to be inclusive and if someone was involved in the project, then I think they should be offered to be co-author (unless it is obvious that their contribution is very minor). It is up to them to decide whether to accept or reject the offer. If you do not like their answer, next time do not talk to them about your work.
Also we are moving to a world where academic work in measured and rewarded very precisely by criteria which are very narrow. For example, in the UK the REF, which measure the performance of departments, in the individual level looks mainly on the quality of papers. So there is little incentive to individuals to supervise students (department as a whole do have some incentive). Now, in most cases supervisors put a lot of work into the supervision. So morally and to encourage people to keep supervising students I see no justification not to give supervisors credit when they deserve it. 
A: Often "suggested the problem, and gave a few helpful comments" can be enough to merit a co-authorship. The student should probably ask his or herself: could I have written this paper without my supervisor's input?
When the student writes on a problem they have suggested to themselves, then the issue is more thorny. I think the standard etiquette is that the supervisor should be offered the option to be named as co-author (and as you rightly mentioned, it may increase the chances of publication, not least because the senior person knows the system better).
A: I believe it to be in bad taste for advisors to co-author a paper with their current student, no matter what their relative contributions. Of course, I am in pure mathematics, and understand that they do things differently in other parts of mathematics, and in other disciplines. Otherwise, there is the possibility of an advisor exploiting their position. This strict policy also obviates any soul-searching about how much contribution is required to be a co-author.
Of course, it is expected that the student will acknowledge in the paper, the help  (if any) received from their advisor.
A: I agree with the answers to the post which state that, as a general rule, the advisor should not be a co-author in the main papers which come from a students' doctoral thesis - for the simple reason that a student's Ph.D. thesis should be the student's original work and not the advisor's work, and authorship should reflect that - but I'd like to add an additional reason which I don't see much represented here, which is the potential for exploitation by the advisor. I've seen cases where a person has become a 'rising star', or even has passed quickly through their promotions and becomes slightly famous, by publishing a ton of papers, even when most (and in some cases as much as 80-90%) of them were from the Ph.D. theses of their students. I've heard anecdotes of advisors holding back deserving students from graduating until they wrote a few more (joint) papers. Both situations I think are exploitative, and departments and the community at large should do more to prevent this from happening.
At a minimum, I think we need to make sure that there aren't incentives for an advisor to gather a large collection of students and then stamp their names onto their papers, and, for that matter, we should really ensure that such practices are disincentivized. In particular, hiring, promotion, and grant evaluation committees should see a disproportionate percentage of papers co-authored with Ph.D. students as a red flag, instead of rewarding it with promotions, fellowships, grants, and awards. Also, scientific committees of conferences should make an effort to invite the (former) students to present their work, and not the advisor, even if the latter may be more famous.
A: One anecdote ... Serving on a university-wide committee, I found that in one field (I think zoology?) the norm is having the advisor as co-author; and when the advisor does not appear as co-author it is taken as a sign that the advisor has a low opinion of the thesis.  
During my career, there are only two Ph.D. theses that were published with me as co-author.   
One case (Yuri Dimitrov):  After the degree was completed, the thesis had to be abridged for publication.  Dr Dimitrov would come to my office once or twice a week and show me his progress (much as he had done before the degree was completed).  In the end he suggested joint authorship for the paper.  Subsequently, we wrote another joint paper extending the work.
Another case (Jeff Golds):  This guy, upon completion of his degree, was raring to begin his career in the software industry.  It was clear he would never publish the work, but I thought it deserved publication.  So I wrote it up for publication, and it appeared as a joint paper.
A: It really depends: I had two doctoral advisors, I wrote papers under the direction of both (separately):  my first supervisor did not have her name on the paper; one of the papers I worked on with my second supervisor is joint, another has just my name (and yet a third has both our names plus a co-author).
The details are boring and not very enlightening, so I won't go into them, but the important thing in that in every case, there was a different, rational and very good reason why the supervisor name did or did not appear. It had to do with the cultural differences between France and the US, publication medium, and how the work was conducted. 
In that respect, the etiquette question is similar as what happens when a colleague chats with you about your current research, or even better when they provide a crucial lemma or idea for your research. You should definitely acknowledge, but when do you offer co-author credit? In that case also, hierarchical considerations can easily come to the fore (if a person is clearly higher then the other in the pecking order, they can easily pass for a bully if they're not careful).
Even the area of math you work with is relevant (I've heard stories of people solving a problem in a group and the paper being published under a single name simply because the culture in that specific field does not give rise to many joint papers).
A: well, that depends :)
For my own students I usually do not insist on being a coauthor. However, in most cases it just happens that one works together on a project which, by accident, is the thesis of one of the persons. In my experience, I had students who worked very much on their own and then they published their stuff alone. Perfectly fair to me. On the other hand, I had students which did not just ask some questions but we really worked together as I would do it with a collegue. So in this case, there was no question that we all are on the paper, sometimes even with a third person. In these cases, the student gets already some flavour of (partially international) collaborations which I believe to be worthy.
For a diploma student (that is a sort of master thing in Germany...) I'm happy if there is a good enough outcome leading to a little paper. Usually, these students are quite happy if they don't have to do it all by themselves.
For PhD students, I have the "rule" that there is a big global project for the thesis which is worked on, essentially in a collaboration. But I strongly encourage the students to tell me that there is some aspect, where s/he wants to work more alone and publish also alone. In fact, for a student aiming at a very good mark in the thesis, I almost expect that s/he has a paper published alone before the thesis is finished.
So, as I said, it depends very much on the situation. I think both ways have advantages and disadvantages. Important to me is that all involved persons feel good about the policy and that things are said in the beginning. Supervising students is always a matter of trust, and this aspect is certainly one of the most delicate ones...
A: The meaning of your question depends very much on who YOU are: a student or a supervisor:-)
My guess is that you are a student.
In which case, my advise would be: just do what your supervisor suggests. Just trust him/her.
Various supervisors have various policies. Some never co-author papers with their students,
even in the case when the supervisor did all work. Others sometimes do, sometimes not.
But my advise is: just do what your supervisor tells you.
A: In my opinion, as a rule the supervisor should not be a co-author in the main paper taken from a student's thesis, even if he has contributed substantially to it, and even more so in the circumstances you suggest. The student needs to publish much more than the advisor does.
If the advisor him/herself is a junior person and has given a lot of help and a very good idea to the student, then I suppose that an exception might be reasonable. Also, a thesis project might spawn more than one paper, of course, in which case it's fine if the advisor is a co-author in some of them (always assuming that he has done much more than suggesting the initial idea).
Of course, it may happen that the student is weak, is given a good project, and needs to be guided step by step, so that at the end the advisor has contributed much more to the thesis than the student. Then a joint publication is in order. Such a student will most likely not pursue an academic career, so it does not really matter.
[Edit] Let me try to clarify my thought, and perhaps be less radical. What I am going to say applies to pure mathematics; I am very much aware that in other fields things may be completely different.
A good thesis project is one that is both interesting and feasible. Devising such a project in pure mathematics is hard; most beginning students, even very bright one, need guidance, particularly in countries, like Italy, where the PhD program is 3 years. A student has a lot to learn before getting to a level to understand and appreciate a research project; it is clear that a student in a short program does not have a lot a time for trying and failing (which is, of course, very educational, but also time-consuming). Now, some students come up with their own problems and solve them, but in my experience they are exceptions.
I consider it part of my job as an advisor to suggest a problem, or an area of investigation that can be profitably mined from the student. After that, I follow the student, teaching her (let's say she's a woman, purely to avoid the "him or her") whatever I can, trying to dissuade to pursue lines of work that seem barren, uninteresting or risky to me, and also giving ideas. Sometimes she will get stuck; and then I'll think about the problem, to see if there is a difficulty that seems unsurmountable, or if there is an approach that she can try. After some time of this, if she is good she will take off on her own, and understand the problem better than I do; then I will consider that I have done my job. When she writes the paper, I will not be a co-author, even if I have obviously contributed a lot to the project.
Of course, different students require very different levels of involvement; but in my experience, it is not necessary true that the best student are the ones needing less help. Also, a lot depends on the problem.
Now, some people tend to give students substantial parts of their research agenda; in this case the advisor is directly interested in making progress, gets more involved, and is more likely to be a co-author. This is another case in which joint authorship is perfectly reasonable. I would not want to conclude anything about a student from the fact that have published the main paper from their thesis with their advisor.
A: Both the ethical and practical sides of the question rely on conventions, and that is the first thing to be aware of. The tricky point is that not all people involved have the same conventions: for example, mixing other answers and comments, an Iranian student and PhD advisor submitting to a French mathematical journal, whose article is read by Gil Kalai will have the authorship question interpreted in three different ways.
I do not have a good way of solving this (except math could start following the path of some journals in other fields, and have a description of each author's contribution mentioned in the paper), and my answer below will be an account of the situation around me. However, as far as hiring is concerned (be it postdoc or tenured or tenure track), it is tremendously important for everyone that an advisor who co-authored with his or her student writes a precise, honest letter stating what are the student's contributions and his or her contributions. I have witnessed recently that the lack of such letter can leave hiring committees in too much doubt to actually consider the applicant strongly. I should add that this advice also applies to famous co-authors who publish with younger colleagues.
In France, in pure mathematics, the convention is exactly as another answer (which is currently the highest-voted one) states: the advisor is supposed not to co-author the main papers of a PhD thesis, except when he had to contribute more than what is expected (which leaves some room for interpretation, but usually suggesting the question, a rough possible angle of attack and relevant literature and having weekly mathematical discussions where the advisor listens and guides not too closely is part of what is expected).
In term of rewards, the PhD student is rewarded by authorship and the advisor by mentioning a advised a (publishing) student in his or her CV (which is sometimes a very important line of CV to have, an unfortunate state of affairs in my opinion, but that is another matter).
One of the points which might explain this convention is that in France it is not exceptionally rare to hire young colleague for a tenured position the year after PhD defense (I can see at least 5 of theses cases this last round of hiring, among 25 new positions attributed). We thus need to have a good confidence in the independence acquired during the PhD, and the co-authorship convention above contributes to that purpose.
To answer Gil Kalai's objection that this convention have unintended consequences, I would say it is true whenever conventions varies or are not uniformly understood. If one wants more precise and reliable information, recommendation letters and talks about the work should give some.
A: When he can honestly claimed that he's substantially contributed in the research undertaking; not merely in the conceptualization, and design but in sharing worthwhile literature, and intelligent suggestions in the analyses of data. In the case of a "serious" supervisor or adviser, I think he would not allow himself to be deprived of such credit. For a beginning thesis-writer, he would really need someone who can assist and provide him proper guidance, and assurance that his work within the University or institutional standards.       
A: In my opinion, from the purely ethical point of view, within the framework of mathematical research, the authorship is of a secondary importance. The issue of the position of the potential authors, e.g. a student versus a supervisor, is, in my opinion, irrelevant. What counts is only that the contributions of everybody, including the potential authors, as well as bystanders (writing/authorship wise), are adequately presented.

If needed, I can say in more detail what I mean by adequate.

REMARK There is, of course, the other question under what circumstances a student, i.e. the student's contribution, should be awarded their degree.
A: I am just a self-taught amateur matematician that has published most of his works alone, but my personal point of view is that a supervisor of a PhD dissertation is worth to be added as a coauthor of a paper related to the aforementioned work, if and only if he has given a substantial contribute to the ideas/concept/proofs of that original research.
Now, some PhD candidates are unable to write a preprint with a proper form (a fact), but this is not sufficient (IMHO) to let a supervisor take the coauthorship of their original work if his contribute has merely been helping the candidate to arrange its own results in a more strict form, in order to let it pass easier the peer-review process.
Just my two cents.
