Pinball games would be a safe bet. So would any non-realtime games - I think Zafehouse is quite fun, despite its faults. Also, Knock-knock have rather simple controls.
If you can deal with light coding, autohotkey can be use to create more obscure shortcuts.

Hidden object games, point-and-click adventures, match-3's and the casual time-management games can be played with mouse-only. I go through spurs when my pain is so overwhelming that I can only play games with one hand, so I've been there; I feel for you!

Making a bald man cry isn't very nice of you.

They've come a long way since Götz von Berlichingen's iron hand (which itself was a big advance for 500 years ago, since it was dexterous enough that he could write with it). And there are still better technologies coming out.

RSL Steeper, of Leeds, made that "Terminator" arm. It's not a one-off; they sell these commercially in the UK and US. The technology is myoelectric: it's controlled by signals from muscles in the remaining arm.

Current research is in "targeted reinnervation", where they can reroute the motor or sensory nerves that ran to the amputated limb and use these to control the prosthesis. Targeted sensory reinnervation will give the wearer closed-loop control, which will be a huge win for dexterity and ease of use.

A joystick would work well for many games that aren't suitable for mouse-only input; for many joysticks the stick portion features three analog axes, a digital hat and six or more buttons. Joystick choices are more limited if your left hand is the one you're using since most sticks are specifically shaped for right-handed comfort.

There are also hybrid keyboard solutions like the Logitech G13 but this would again depend on which hand was affected.

Pedals would also work to gain extra inputs, as iippo already mentioned, and could be used in combination with any other control method with a bit of effort.

Light gun shooters. Sadly not many around anymore, I think House of the Dead: Overkill was ported to PC not that long ago, though. May sound like a crappy suggestion but I actually always enjoyed the series, even playing it with mouse on PC.

LOL I thought this thread was going to be about enjoying Tomb Raider on more levels than the designers intended, maybe with the aid of THOSE patches! :-D

No, but I sometimes use a mouse and keyboard with one hand.
Ya dangus! Beat me to it.

Learn how to play with your feet .

Racing games with WASD or Arrow keys could work

I was a part of weekly Halo tournaments for a long time and one friend who regularly showed up gamed with one hand for about a year or two. He got his arm mangled in farm equipment. I hear he's much better now (I moved away).

He was regularly a top 3 in the games (out of 12-16). And he played with the controller up to his face. My memory is fuzzy on exactly how he did it. And it was an original XBOX, so it had those big controllers. I remember that he used his mouth on one of the joysticks and stretched his hand across the controller to reach the other joystick, D-pad, buttons and triggers. It was goofy looking, but if you mocked him, he'd kill you. :)