EDIT: My hand is no longer sore but feel free to recommend games anyway so that other users can reference to this thread if they ever have a similar problem.

My left hand has been sore for a while so it's painful for me to play games for an extended period of time. I'm looking for games that only require 1 hand and preferably the right hand.

I'll give away 250 Viz per a game that you recommend and 1000 Viz if it's a game I end up playing (Viz offer no longer valid). It can be a game for almost any system (Xbox 360, Wii, 3DS, etc) and it can be a game in the RGR as well. Please no PC or mobile games but you may suggest Windows Phone 7 or 8 games.

Games recommended so far:

Multiplatform
-Tetris
-Pac-man
-The Impossible Game
-Pong
-Super Monkey Ball
-Donkey Kong
-Popeye

3DS
-Pokemon Art Academy
-Pokemon Trozei
-Colors 3D

DS
-Phoenix Wright
-Ace Attorney
-Rhythm Heaven
-Cooking Mama
-Nintendogs
-Bomberman Land Touch 1 & 2

Nintendo NES
-Bomb Swepper
-Duck Hunt

PS Vita
-Grim Fandango

Wii
-Bit.Trip
-Wii Sports
-Fishing Master: World Tour
-Zack & Wiki: Quest for Barbaros' Treasure
-Mario Super Sluggers
-Beat the Beat Rhythm Paradise
-Art Style: Orbient
-World of Goo

Others
-Most RPGs
-Most Card games
-Some Pinball games
-Some Flash games
-Some "Break Out" clones
-Runner
-Beat and Flux
-Beyonetta
-Fate/Stay
-Just Dance
-Temple Run
-Five Nights at Freddy's
-Happy Wheels
-Hearthstone
-Car Mania
-Doom Warrior
-Blendoku
-Art Style: Cubelo
-Hotel Dusk
-Scribblenauts Remix
-Plants vs Zombies
-Pokémon Shuffle
-Finger Death Punch
-Mirror's Edge (Mobile)
-Despicable Me Minion Rush (mobile)
-Radiant defense (mobile)

One Finger Death Punch is really fun and only uses two buttons.  It's available on steam or on the xbox 360 ($4.99 on steam, and $2.99 on 360)

Civilization 4 or 5.

SpinDrive : I should've mentioned non-PC games unless they use a controller.

nakina : I might check it out.

Davideo7 : Pretty sure pokemon art academy just came out and its one handed. the Pokemon trozei games are one handed too. Also, Mario paint is with he mouse adapter. Lots of puzzle games can be played with 1 hand too

Mortal Kombat! Kidding, kidding.

There's a neat Android game, I think it's called Moonjumper or something. Moon run? Hmm. If you have an iPhone or iPad, I'd also suggest Mirror's Edge. The gameplay is very different from it's console/PC version, but it's still similar in style and theme.

Also, sounds like you might want to go to the doctor's. Sounds like it might be more serious than a simple sprain

pac man you can just use the arrow keys

It has been awhile but I am pretty sure you can play Suikoden 3  for the ps2 with one hand has you can move the character around with both analog sticks.

Wii Sports has many games you can play with just one hand... All of them in fact, except for Boxing. Otherwise Wii Play has several games that are played using only one hand, shooting, air hockey, fishing, etc.

Hmmm... I THINK you can play Chrono Trigger DS with one hand if you use the DS touch screen. You can also play The World Ends with You on one hand, though you will have to leave your partner on auto

Davideo7 : Wow! You want a one handed controller game! Ummm...PacMan? You could change the controls so the arrows are buttons. Games like Bosconia and galaga should also work with that method. Wii is a good system for one handed games, unfortunately the ones that I know are not that great . Space camp and Cooking Mama should both work fine. It's sort of difficult because the movement stick on most consoles is the left one! If you don't want to hurt your thumb, is it? Don't play Metroid Other M (especially in hard mode) or super Smash bros! Outside that there is not much that I can think of! 

No need to send the viz, if you do not want to, I have all that I need for now (if you do not count the fact that I accidentally replaced the sword of vizzed trying to get a second weapon!)

i can think of a ton of games that can be played with one hand but their ment for two hands but are very simple and usully untimed, for 3ds animal crossing new leaf,and in rgr fatal laberinth (some sega thing in rgr), the adventures of lolo(nes), othello(any),any tetris game,any of the dragon warriors for nes, any final fantasy that dosn't require extra movement so most of the classic ones,any one of the fire emblems

Pokemon. Any of them.

Seriously. It may not "strictly" be a one handed game, but if you play it (especially on Vizzed! RGR Plugin Plug!) you won't need to worry about making quick decisions. Being a turn based RPG, it's slow moving and only requires one hand.

I wouldn't advise playing a physical copy, however, unless you feel like putting the handheld down.

Davideo7 : For WIndows Phone 8 I would recommend Despicable Me Minion Rush and Radiant defense.

Why would you limit yourself to non-PC games when you could play some real gems on PC with your mouse hand? Planescape Torment, Baldur's Gate 1 and 2, and Divinity: Original Sin. They're all so good.

I second Leggy's comment. I had a problem with my wrist for a while, and Pokemon was my favorite game series to play one-handed during this time (the more recent Pokemon X and Y might be more frustrating, though). I'd also recommend Pokemon Trading Card Game for a nice diversion. Also, if you're into art, I recommend Colors 3D for the 3DS. It's gotten brilliant reviews, and is a fun way to pass the time.

Also, Fire Emblem (any). They will keep you sucked in for large amounts of time, and are perfect for those who can only use one hand.

I would probably say any rpg would be playable.

Warioware games usually only require 1 hand too.

the classic pac man you just use the arrow key

Definitely Tetris. As soon as I saw the title to this thread, I thought of Tetris. There are also lots of Wii games (Mario Kart Wii w/ the Wii Remote instead of the GC controller, WarioWare Smooth Moves, etc.). Hope I could help!

The old school Mr. game and watch watch put that bad boy on one wrist and let that hand rest, while the other one goes to town, also the classic donkey Kong game can be played, as well as the old school Popeye game in the arcades.