I do keep a nail clipper in my desk, but it's only for the ocassional hang nail or clipping an errant thread off of clothing. I don't use it for regular nail clipping.
I suppose some people keep nail clippers in their bags or desks, but it never even occurred to me to have them at work. I have a nail file in my purse if I break a nail. I think doing it at work is more gross than it is rude.
I keep clippers and file in my desk, it's handy if a nail breaks or catches and snags. I don't clip/file when coworkers are around (agree that it is rude due to the sound) and always do it in my trash can. Toenail clipping in the office on the other hand is 100% unacceptable.