I'm starting to notice a lot of build-up on my bass's fingerboard, as well as on the body itself (from rosin). What do you guys typically use to clean up your basses without damaging the fingerboard/finish?

For the fingerboard, I use a silky or synthetic fabric type rag to avoid having any lint. Usually fingerboard grime will come off fairly easily with some hard rubbing.

For the body I use a good violin polish/cleaner like Hill Polish, Salchow or Viol applied with a very soft cotton type rag. There are also some other good violin cleaners out there. They are expensive but the good thing about them is that they are fairly safe to use and won't damage your precious instrument if used as directed.

To get rid of fingerboard grime, I use #0000 steel wool and a little of Kolsteins instrument Cleaner. Works Great on rosin buildup, and if you are apprehensive about using steel wool, 3M makes several different grades of scrub pads you can use instead.Then, after you clean the fingerboard and body, polish it with Either Hill Polish, Kolstein Polish,or the others mentioned. Use a soft Cloth (a t-shirt works great).

After you've cleaned the bass in the manner these other fine bassists described, get in the habit of wiping down the bass when you're done playing.