My left hand can't be used for gaming. Suggest me what to do

Fap.

Also, Dungeons of Dredmor.

Read a book.

Any point and click adventure game, a lot of older RPG's.
Fallout 1/2, Baldurs Gate 1/2, Icewind Dale 1/2, I think Freedom Force as well but I'm not sure on that.

Anomaly: Warzone Earth
can be played using mouse only.

Play tf2. I did when I dislocated a part of my hand. Just bind forward and jump to the mouse and you are ready to go (if you are good enough)

Modern Warfare 3

Buy a mouse with more buttons, also you can grab a USB Controller and map (with Xpadder) the keys to only the right side. It is going to be awkward but you don't have too many options.

Jamestown can be played with the mouse only

Audiosurf, Magic The Gatherinc Duels of The Planeswalkers 2012 and fapping.

Just play facebook games :)

Mirrors Edge

play facebook games :)

How about just watch some movies? or some racing games where you just use the arrow keys?

Well you don't have much games to choice play:

Crayon Physics Deluxe

Hammerfight

Revenge of the Titans

I would say any turn-based strategy would work, though take a bit longer to the point it'd be best to play against AI. Tower-defense games that give you the option to pause could work as well.

Well, here are some options based on your game list:
And Yet It Moves
Atom Zombie Smasher
Cogs
Loom
Machinarium
Revenge of the Titans
SpaceChem

I think maybe Atom Zombie Smasher can be played with one hand.

Crayon Physics Deluxe

Cogs

Loom

Machinarium Maybe

Spacechem

Depending on how long-term this problem is going to be, you may want to look into a device known as a Twiddler (which no, before anyone comments on what that name sounds like, has nothing to do with fapping).

It's essentially a one-handed device intended to take the place of a full keyboard and mouse. I know that sounds like a huge aim, but its 'chord' approach of assigning letters to combinations of buttons held down at one instead of individual keys apparently works quite well for typing, once you've had a little practice.

Unfortunately I suspect that that way of working might mean that to, say, hit 'jump', you would have to first take your fingers off the combination for 'move forward', which would make a lot of games unplayable on it (at least without a carefull bound multiple-button mouse). I honestly don't know, sorry. I've been after one of these things for a while, but never gotten around to facing the hassles of trying to get one shipped to where I live.

Look it up and see what you think. Or don't bother, if this is just a short term problem not worth the expense.

Other than that... puzzle games. Lots and lots of point-and-clicks and puzzle games.

There's a product called TrackIR - a mouse-replacement where a camera on your monitor follows your head movement. When I trialled one a few years ago, it was no good for FPS gaming. But I think they're much better these days, so might be worth looking into at least.

And Yet It Moves.
Just play that for the time being.

If you are right handed then many startegy games require only mouse. Plus if you want to play just for fun all the dota type games require really only one hadn and we cant forget about all the point n cick titles.

I see no mention of the original starcraft or warcraft 2.

7th legion if anyone here has heard of it...

Minesweeper/ solitaire

Sim city, insert name here tycoon, CIV 1,2,3,4,5? C&C, AoE, Tzar, Risk, Monopoly etc etc etc etc..

Fix your left hand

play Kings Bounty if your into turn based strategy
awesome game (especially crossworlds) and is mouse only

Star Wars KotOR. Not having it is not a valid excuse. Go buy it right now.