My cat actually started eating litter back in December. I couldn't believe my eyes when I saw her eating it!! Definitely don't use the clumping litter, as that can cause all kinds of problems in a cat when they eat it. I was able to get my cat to stop by very closely watching her whenever she went near the litter, and if I saw her attempting to eat it, I'd call her name so that she knew I was watching her, and she'd stop. Of course, you can't say "No" because you don't want them to think that it's bad to go to the bathroom in the litter box! But my cat did eventually stop and she hasn't done it since. I never figured out why she was doing it! She was having really bad stomach problems at the time and all the vet could come up with was that maybe, for some odd reason, my cat thought the litter would make her stomach feel better. Very strange!
We tried the Yesterday's News brand litter - it's basically hardened newspaper and is digestible if cats decide to eat it. It is expensive, though, so as soon as my cat stopped eating it, we slowly switched back to the old kind we were using.