I don't keep them. I rip them up (one time I ripped the check instead of the stub - oh oh). Anyway, I am the controller where I work, so they are in a cabinet right behind me if I need them.
I used to keep them forever, what a waste. I think if I did not have ready access to them, I might keep them until I got my W-2 for the year - just because I am a little bit of a pack rat.
I think someone should keep at least the last couple of check stubs, especially if you are considering applying for a loan, applying for public assistance of some sort, or going through a divorce / child support proceeding. You would not believe the number of people in the middle of doing those things who come to my office looking for copies.
Denae