Should I not cite an arxiv.org paper which otherwise seems to be unpublished? I want to cite a paper which is on arxiv.org but is not published or reviewed anywhere, and no publication or review seems to be in the pipeline.  Would citing this arxiv.org paper be bad?  Should I wait for a paper to be peer reviewed before I cite it?
Added:
I don't actually know whether a 'real' publication is in the pipeline.  The alternative to citing the paper would probably be to ignore it; I have a way to extend the results in the paper if the paper's results are true, but I don't have the skill or time to verify that the arxiv.org paper is correct.
 A: My advisor and I have referenced discussions here on MO in our latest paper,
so why not arxiv?
A: [It is] Not really [bad to cite an arXiv paper]*. If the paper on arXiv provides the result you want, you are free to cite it. Before the arXiv, citing "private communication" or "pre-print" is not unheard of. On the other hand, since it hasn't been peer reviewed, you probably should double check and make sure you understand and believe the paper before you cite it (if you use one of its results crucially) (not that you shouldn't do the same for peer-reviewed papers, just that one may want to be extra careful with referring to pre-prints). 
Note that there are two reasons for citations. The first is to give credit where credit is due: you do not want to look like you are appropriating someone else's result (or in some cases, inadvertently slighting somebody by sin of omission). The second is to provide references for assertions made without proof in your paper. Obviously if you are citing for the former reason, a paper is arXiv is really no different from a paper in a published journal. If the author's right, you covered your bases. If he was wrong, then better for you, perhaps. It is with the latter case you need to be more careful. If the paper has been on arXiv for a long time and not appeared in any journals (definition of "long time" of course vary from field to field), you may want to be a bit cautious in deciding whether the foundation to your house is sound. 
Also, how do you know "no publication or review seems to be in the pipeline"? I know several people (myself included) who would only include the journal ref on arXiv after it has been accepted for publication. Perhaps you should double check with the original author whether it has been submitted, and if not, why not? 
* As Joel pointed out in his comments to the original question, and Emerton in his comments to this answer, there is some ambiguity as to which question I was answering.
A: As has already been noted: there are two reasons to cite a paper, an email, a letter,
or anything else:
(1) To give credit.
(2) To refer to a result you need.
If a citation is for reason (1), you should cite anything and everything that is appropriate.
If someone explained a result to you in an email, cite them, or at least acknowledge them in the paper.   If you rely on the results of a preprint, or a preprint proves important results germaine to your own work, you should cite it (whether it appeared on the arxiv or not!).
As for reason (2), it is up to you.  In general, you shouldn't be relying on results unless you are confident that they are true.  Typically, it is up to you to determine your own threshhold of confidence, and if publication in a peer-reviewed journal increases your confidence, you can take that into account. But in this context you must still take into account
criterion (1): i.e. even if you avoid relying on an unpublished result out of a sense of caution, but that unpublished result is closely related to what you are doing, you
should still mention it. (A typical situation might be that you need a special case of
an unpublished result that it is easy for you to prove directly, and you prefer to do so
rather than rely on the unpublished result; then you can certainly do so, but you should
point out that what you have proved is a special case of the more general result, and cite
that more general result.)
One thing to note is that some journals may not accept your paper if it relies crucially on unpublished results (including unpublished results of yours!).  Thus, if you rely on such results, you may want to include a sketch of the proof, so as to make your presentation somewhat self-contained.  In this case, if you giving a sketch of the proof of someone elses result, be sure to include appropriate citations from category (1) above!
A: Be careful with papers which claim to solve important problems but have been on the ArXiv for a long time with no sign of a journal version appearing.  Ask the author what is happening. The reason might be that journal referees don't believe it, in which case you probably shouldn't either. This situation is not rare.
A: People have been including cites of the form 'preprint Year X' for decades. Simply citing 'preprint Year X, arXiv:0000.0000' is not a huge leap away from this traditional and well-established behaviour. Indeed it is clearly better than it.
A: Why not? I saw citations that looked like: "[42] J.Smith. Private discussions."
These are definitely not peer-reviewed...
A: I agree that citations to arXiv are useful because this is an open and accessible online resource unlike most journals or conference proceedings.   But papers should be identified as preprints if no refereed version is known to exist.  (Indeed, there is a long tradition of citing preprints or even personal communications.)  An important caveat is that many arXiv posts are later published in improved versions, using feedback from referees or others; but the last version you see on arXiv is not necessarily the final one.    Sometimes significant errors are corrected or important citations added only in the published format.    
A: I think you should always cite a paper on the arXiv, if it would be appropriate to cite the paper at all.
I want to strongly encourage people to put preprints of the arXiv.  It makes mathematics more open.  It's incredibly useful for following what's going on in fields not quite your own, or if you are not in personal contact with everyone in your field.  However, I know mathematicians who do not put preprints on the arxiv (or only do so just before publication) because they are worried about "losing citations".  Sadly it seems that many funding agencies and universities are starting to use citation data; so it will become more important for citations not to be "lost".
Thus, it would seem that a culture of not citing arXiv papers (just because they are on the arXiv) is going to encourage people not to use the arXiv, which I think is a bad thing.
Of course, as Willie says, you should be very careful about proofs.  But, as other questions on MathOverflow have suggested, just because a paper is formally published doesn't ensure that it's correct, and not all referees carefully read proofs.  So, you should always be careful.  Also, it takes so long for the refereeing and printing process to happen that quite often, what starts out as a reference to the arXiv will become a reference to a published paper, by the time your paper makes it to galley stage.
I would agree, though, that if a paper has been on the arxiv for a long time, but seemingly hasn't appeared in print, then you might want to be extra careful (and under such circumstances, I think actually writing something to warn the reader would be okay).
A: I would definitely cite the arXiv paper, though taking care of the particular version of the paper from arXiv that I am citing, because several authors do update their arXiv submissions occasionally. As also pointed in responses above, how would you still use the result (or build on it), if you do not cite the arXiv paper? 
I guess your worry might originate from the fact that some reviewers of your paper might not duly appreciate your theorems, their value, or their correctness, unless you build upon peer-reviewed material. But for want of a better alternative, it is still better to err on the side of "correctness", and cite the most original source that you can track down.
PS: On a related note, I would even cite MO if I had to use a result that someone showed originally showed here (several such examples exist I guess).
A: It is clearly stated in all licences in arxiv (and in preprint arxives and publishers elsewhere) that the works by others published on arxiv or elsewhere must be cited when used. But most important is that if results have been publicly announced by the author in a publication as preprint research report on arxiv or elsewhere, and one knows about that, then one honestly do best to cite other works  from the moment they first appeared publicly on arxiv and elsewhere as soon as one knows that and especially if there is overlapping result, examples or other relevance of the new notions or considerations published in the paper that are relevant to your results and publication. If there is a mistake in a published publicly in arxiv or elsewhere paper then one can either correct it in own publication and cite the orignal published (=publicly made available for others than the authors (green open access as arxiv etc or in other publications) paper, and explain that there is a mistake without informing the author in private communication (this is hardline formal way since the author will know that only when it finds your paper somewhere some time in the future and also you might be wrong and thus will create stress and bad health wrongly to the authors if you do that way), or better simply send an e-mail or call and ask the author on this first as a colleague letting the author to check that and give a feedback with thanks since it can be for example also not a mistake but a misunderstanding from the readers side. Other time you might be in their place with someone else claiming (possibly wrongly) a mistake in your work, etc .... Life is long and complex and many things can happen in many ways .... Better to be "all winners" then "all losers"! :)
