One handed games

Audiosurf :)

Atom Zombie Smasher is a pretty good one handed game. Super Meat Boy is tough as nails but can be played one handed.

World of Goo only requires the mouse, quite fun puzzle game if you're into those.

:3 my poor Georgie <3

Anyway...

Most popcap games if I'm honest / casual games

Peggle comes to mind ;) and Chuzzle..OMG CHUZZLE <3 haha

You still need to check out your Penumbra games, not sure about them

A.R.E.S

Abe's Oddysee (I think?)

Point and click stuff > Telltale games, Sam & Max, Secret of Monkey Island etc

Bad Rats ;)

Umm..Your Doodles Are Bugged!

Most poker games

Trauma...which I know you love so damn much ;) lmao

Sunnyville: Hidden treasures (and allllll hidden games)

Itza games :D I'm such a big child and bought them during the sales haha "Can you draw a house?" Yes, yes I can draw a house! ;)

The Luxor Games (Mahjong etc)

I'd imagine B.U.T.T.O.N but never played it

The Political Machine may be 1 handed

EDGE (awesome game btw)

Runespell: Overture

Secret of The Magic Crystals :D you need more screenshots ;)

Who Wants To Be A Millionaire? (Eventhough the game is bugged to hell and doesn't work for me -_-)

Zen Bound 2

And that's about all I can think of right now lol, sorry hun

CoD MW3. Just use your mouse to aim. No one will notice you don't/can't move, as they are all campers.

World of Goo,
Civilization V,
and Diablo 2 if you can get it somehow. (If you do, try to get the Lord of Destruction expansion as well)

That's all I can vouch for and hope you get better!

Boarding sure thing

Deponia, although the ending made me sad.

Go for Defense Grid: The Awakening. Such an incredible game if you have any interest in tower defense :)

Cubemen, Bit.Trip Runner, Rush, Edge, Critical Mass, maybe LIMBO...
...and MARIO!!! I played this on 1 hand and thats cool! :) (Mario 64, you can emulate it xD)

Minecraft

I did kill a lot of time with Poker Night at the Inventory, one handed and funny. Then one of your best bets is games like visual novels or a point and click adventure.
A few examples on steam are Analogue: A Hate Story and Ceville respectively, you could consider it is you like those kinds of games.

Torchlight
Simple platform games
Pokemon.

Starcraft 2, Quake 3 Arena, Counter Strike: Global Offensive,
especially on Multiplayer

Civilization / SimCity / Machinarium

Team Fortress 2. At least I dominated servers with all the 5 possible buttons on my mouse.

Revenge of the titans
Atom Zombie Smasher
Defense grid: the awakening !!! (look my giveaway! :-p)

Progress Quest. you won't even need one hand to play that game.

Most arcade racing games can be played with one hand on the keyboard.

Magic the gathering...pretty much all card games...Sam and Max and all "point and click" games....all Trackmanias and...that's it

Many games can be played one-handed, by adjusting controls.
All pre-Quake id Software games.
Arcade racing games like Need for Speed series.
Every game where it is possible to play with mouse only, even though it makes it harder. Like strategies, FRP's, 3rd-person adventures, puzzle games (or with keyboard),...

"Yesterday" is very nice game.

Audiosurf
Swords & Soldiers HD
Diablo 3 (But it sucks, thats why you can play it one handed)
Atom Zombie Smasher
Every turn based/non real time Game
Flight Control HD
From Dust

You could try to play Dragon Age too,but you need the space button ^^

Almost every Browser Game

PvZ

Minesweeper