I play a lot of Wii sports and my wrists hurt. Is this a coincidence?

Probably not Lando! You can easily overstress joints and tendons with these kinds of activities. A few years ago  doctors coined the name 'Nintendo thumb' for people who hurt their hands playing on the old-style controllers as so many people were developing problems from too much gaming.

I am no doctor (in the medical sense) but I would cut down on playing so many games if I were you and if you still have problems go and see a proper physician. You could cause real long-term damage if you play too much!

agreed (and I am a medical doctor - Dave is a proper doctor!). The other name for what you are describing affects many people in various walks of life - it is called RSI (repetitive strain injury).