I noticed that I often get a bit of numbness in the left hand but never in the right hand, especially when cycling in the plains. But guess what: I'm often shifting the rear derailleur (right hand) but rarely the front one (left hand), which means that my weight is often carried by the left hand while the right hand is busy at shifting. If I think about deliberately taking my left hand off the handlebar once every 15 minutes or so, I'm ok.
DOH! I was wondering why only the fingers on my left hand were going numb! Ding dong...
I fixed my wrist/hand problems by getting a shorter, steeper stem, which allows me to use my abs and back to hold me up off the handlebars a little, I got VERY thick gel gloves (PI Gel-Lites). I've got a Trek 1000 (road bike) with flat handlebars, so I added those longish bar ends, and I have them sticking out straight in front of the bars, and I use them sort of like wide aerobars. Gives me some extra options for hand placement (which I change a LOT), as well as getting me down low so I can go faster. And about every 10-12 miles I shake my hands out really well.
This has helped 80% of my wrist pain and finger numbness. My next step is to get a saddle that I sit square on. My Terry Liberator isn't flat across the top and I tend to roll down off my sit bones into the valley, even with the nose a little higher.