I have a friend who I do l4d2 with occasionally, who only has one arm. We play realism expert mode, and run & gun most of the levels. So I'm going to have to say that pretty much all games are possible if you put in enough effort.
Granted he's lived with it his whole life, so he likely has an advantage in that regard.
Games that are the easiest to play one handed though, I would say, are:
IL2 Sturmovik (Original or Cliffs of Dover) | Flight Sim
Starcraft 2 | A lot of the custom maps can be quite fun, and fairly easy to play laidback with one hand
Aventure games like, Monkey Islands, Space Quest, Kings Quest. Some of the newer ones like Gemini Rue, Sherlock Holmes collection.
Simplified RPGs that use turn based combat or are excessively easy. KOTOR 1&2. Arcanum, Fallout 1&2.
Turn based grand strategy games like Civilization, Hearts of Iron.
I'm sure racing games can also be played pretty easily one handed, but I really don't like racing games that much(I didn't even register my free copy of Dirt 3 or whatever, despite it having like a 50$ value) so you're on your own there.
As far as FPS games, you're going to have difficulty finding something easy to play. You could make a modified setup if you have a mouse with quite a few buttons, to make everything easier(IE RMB is run forwards rather than using WSAD). But strafing will still be a problem so I'd recommend single player or coop games only.