Suppose you're an video gamer who just broke a wrist. You'll be out of the game until it heals, right? Not necessarily. The Nintendo Wii library features many games playable with only a single hand and the folks of Ask MetaFilter are listing their recommendations.
Endless Ocean lets you swim around the open sea, caverns, and sunken ships. It's a little "non-gamey" in the sense that you cannot die and you cannot fail. You can move it's limited plot forward at your own pace, but the meat of the game is just swimming around and seeing different types of fish and sharks. As far as controls, movement is controlled by the IR in the remote (swim up by pointing up, swim down by pointing down (or can inverse that with a settings toggle)). Also, you can shake the wii remote to pet fish, if you'd like. I liked it, and my girlfriend loved it, but YMMV.
Zack & Wiki is a point-and-click adventure style game that is chunked into a number of levels, with each level being centered around an environmental logic puzzle. It's a very cute game, but unlike a LucasArts type adventure game, timing becomes pretty central and you will die frequently. Although a character's on-screen movement is controlled by pointing the remote and pushing a button, there are some segments were wii remote movement is involved. I forget most of them, but one of the early ones has you move the wii remote back and forth horizontally to saw down a tree; I don't think any of these segments would be difficult to accomplish with one hand.
I know I've played plenty of Wii remote-only games, but I can't think of anything worthwhile at the moment that relies on just the pointer functionality that hasn't already been mentioned in the Ask MeFi topic. Remember that a broken wrist means that it's not practical to use the controller in the old fashioned Nintendo Entertainment System configuration. We're talking about just point-and-click here.