Curriculum vitae:  including grants you've applied for, not received (or not yet received). I've heard from multiple sources now that one's CV should include grants you've applied for, even if you didn't receive them or won't find out if you've received them until after your CV goes out.  I haven't had much luck finding this in other people's CVs, though.  I'd like to have confirmation of this from someone who's been on a hiring committee before.  If this is the case, any advice on how to present this information?  (example appreciated as always).
General advice about CVs is appreciated too ...
 A: I've never (through hundreds of applications on several hiring committees in math and one in statistics) noticed "grants applied for", although I wouldn't put any weight behind it if I did see. Perhaps I have seen it, and forgotten it just as quickly.
"Papers submitted" carry some weight, but only if you've made it to the short list and we are going through your app with a fine tooth comb. In that case, having the article available on a website is good (we can take a look ourselves), but having it on the arXiv is best. It signifies to us that you are modern, self-promoting, and that you are proud enough of the work to make it available to your peers.
We sometimes see "junk info" on CVs: things like "avid frisbee player", "concert pianist", and such. It doesn't influence our thinking, but it does give us a way (within the committee) to refer to the person. "Well, unpronounceable name does have 6 good publications, and the dog person only three, but Dog's letters read much more strongly."
When I was first applying, I had been attending (and sometimes speaking at) conferences as a grad student for many years. I figured that there were people who knew me, but wouldn't know me by name, so I put a picture of myself on my CV. I'm still getting teased about that, so I don't recommend following my lead. Then again, I did get offers...
A: First, let's assume that you're applying for a position, where your research matters. If so, then the hiring committee wants to judge as best as it can whether you will do good research after you're hired. Also, let's assume that the hiring committee is not familiar with your specific area of research, so it is not able to judge directly the quality of your work by reading it.
Published and accepted papers, as well as grants awarded, are very useful for establishing the strength of your research ability. Other measures such as quality of journals and citation numbers can strengthen your case even further and are in fact quite important if you are applying to a strong department.
Submitted papers, preprints, and grant applications do not help in judging your research ability. But they do matter. In particular, they, along with the items above, show that you are committed not only to continuing your research but also documenting it in a way that your department, your university, and your peers can judge it properly. In short, it provides evidence that you're willing to and are continuing to "play the game". This stuff won't help you beat out someone who is viewed as a stronger mathematician than you, but it might help you beat out someone viewed as on the same level but does not demonstrate the same level of explicit effort.
You should provide all evidence of research activity, whether it represents something you've already accomplished or something you are still striving for.
And you should omit anything that a hiring committee might choose to interpret as a serious distraction to your research efforts.
A: I completely agree with what Richard said.
Since you asked for "general cv advice", I thought I'd list some things that people often put on CV's that I think shouldn't go there.  Some people might disagree with things here, but what's the internet for if not making controversial statements?
1) The places where your papers are submitted.
2) Undergraduate honors other than various flavors of "cum laude" (ie membership in Phi Beta Kappa).  The only exceptions I would make here are Putnam fellows or the Morgan prize for undergraduate research.
3) Membership in professional societies like AMS/MAA/AWM unless you have some kind of official role in them.  For instance, it would be appropriate to list it if you were president of your local chapter of the AWM or if you served on a committee for the AMS (I know of at least one postdoc who has done so).
4) Too many papers "in preparation".  It's ok to have a couple of papers listed as "in preparation" if you actually have some kind of draft written.  However, I have seen cv's in which the author has more papers in preparation than written/accepted.  This definitely looks like padding.
5) For a graduate student, it's probably ok to list talks in the graduate student seminar or your thesis defense.  However, once you have left graduate school these should probably disappear.
A: You have a certain amount of leeway as to what kind of material you wish to include in your CV.  I have seen things on CVs that were of little or no interest [edit: here I actually meant "of interest to me as a potential hirer", not personal interest]: high school honors, nonmathematical awards, etc.  It doesn't make me think less of the person.  
I would say that it's within reason to include a grant that you have applied for but not yet heard back from.  You are inviting the reader to compute an expected value, which will presumably turn out to be positive.  This cannot be said for grants that you have definitely not received, and I wouldn't normally recommend that someone put that on their CV.  Still, I could imagine cases where that might be appropriate: for instance, at many research universities, given that you don't have a grant, the information that you have at least applied for one every time you had the opportunity might be looked upon favorably: ask a trusted mentor about this.    
A: I've served on tenure-track hiring committees.  Notification that you've applied for a grant wouldn't work for or against you at our place, as far as I can tell.
I wouldn't in general include where you've submitted your papers.  Maybe there's an exception if the paper is joint with senior person X -- in that case there's an implicit guarantee that Prof. X thinks it's a JAMS-level paper.
A: I am in exactly this situation right now: on the job market, with a paper submitted to JAMS a year ago and not yet accepted or rejected. So I am listing it as "submitted to JAMS, 2008" on my CV, partly just to indicate to whoever is reading my cv that I think that this is one of my strongest results.
