I'm left handed so I wear my watch on my right wrist. Most left handers have to be somewhat ambidextrous. I throw with my left hand and write with my left hand but I golf right handed. I know that they make a lot of things for left handers, including watches, but most left handers don't have a problem with right handed stuff like watches, scissors, guitars, etc.
Now that I'm over 50, it probably doesn't matter which wrist I wear it on unless I'm playing tennis. I don't wear a watch when I play tennis.