I agree with Elsie that many yoga routines rely too heavily on the down-and-up-dog sequence. But keep in mind that a very traditional and time-honored routines are the Primary Series and Sun Salutations, which are extended versions of that. Wrist problems are, I suppose, an occupational hazard for yogis - all of the cool arm balances, etc.
That said, I just don't do them. I have several yoga DVDs that I used to do. Now I use them for ideas if I need a refresher, but I always put together my own routines, based on the standing balancing poses (like tree pose and the warriors), and lots of stretching/flexibility. My wrists are arthritic and can't handle the popular routines at all. But yoga is so incredibly flexible (pardon the pun), that anybody can reap its benefits, as long as you're willing to listen to your body and think about the poses that work best for you.