Fishing Master: World Tour for the Wii has simple controls that are kinda wrist flick-y but only require the full use of one hand. I hate fishing, but this game has a kind of cartoon like theme and I found it to actually be quite fun.
Also, there was a Pokémon Arena game for the Wii, though I can't remember its name. But it had simple controls where you would consecutively battle one trainer after the other. It had cool bonuses like porting your DS Pokémon and then being able to buy items in game through earned points which could then be ported back to DS. This game was slightly childish, but it was a fun time waster nonetheless.

Davideo7 : happy wheels for PC (Google it and you should find a link)you simply need arrow keys on the key board.

Davideo7 : Have you tried Wii Party or  Wii Play Motion? They are pretty fun, just a bunch of mini games thrown together.

I have a few they could taken but what the heck

House of the dead {PC only a mouse though}

House of the dead 2 Wii

House of the dead overkill Wii }depending on your age[

Resident evil umbrella chronicles Wii [nun chuck not required]

Resident evil darkside chronicles Wii [nun chuck not required]

Dragons Quest Wii

The Grudge Wii [controls might be difficult]

Bioshock Wii [nun chuck not required]

Goosebumps Wii [nun not required for some games]

Ghostbusters Wii


I hope your hand gets better and you'll enjoy them.

Try Bomb Swepper, an excellent conversion of nintendo´s game & watch classic.
It´s a NES game

I'll say Wii Sports.It is one of the best-selling video games of all time after all

Maybe you could try Crypt Of The Necrodancer. It's a PC game that plays with 4 buttons and can be played with a controller (I believe you can choose the controls yourself, so you can use the A,B,X,Y buttons or the D-pad) or even a dance dance revolution dance pad if you happen to own one of those It's a quite simple but an incredibly fun and addictive game with great music.

I know you said no PC games, but since it's meant to be played with a controller, and the A,B,X,Y buttons are very much viable I figured I'd recommend it anyway. You might have to fiddle a bit with the control settings since pressing for example X+Y at the same time to place a bomb could be a little bit awkward but it should be doable. Alternatively I suppose you could play it with all fingers on the buttons, like you would on a keyboard.

Other than that there are a bunch of card games that you could play with one hand. Uno for example on the Xbox or Hearthstone on android (it just released on android yesterday actually) or poker if you're into those kinds of games.

Davideo7 : I don't know if this has been recommended before....... But you can play Five nights at Freddy's with one hand, if you care about that game at all. If not, you could always play ninjump, or tiny wings (Don't worry, it's not a flappy bird clone. ^.^) on mobile. EDIT: I'm pretty sure that the two mobile games I mentioned are on windows phone. Their both arcade-style games, and worth checking out. Also, lost winds is a really good one handed game..... Sorry, there's just ALOT of good mobile games. Uhh..... Rythm heaven (DS and Wii) is a really good game that you don't need two hands for.

How about a 1 button game? The Impossible Game uses one button, jump. ($3 X360 with 1 level and $3 for the other 4, $3 for 1 level on mobile and $1 per level for the rest, $3 for all 5 levels on PSN (PS3, PSP, Vita, maybe PS4?))

EDIT: Or you could play just about anything with a one-handed controller. You have get those special made though (or make it yourself).

Here are some good RGR games that only require one hand:
Levers
Pac-Man
Duck Hunt
Hogan's Alley
Wild Gunman
Rally-XNew Rally-X (if you keep the smokescreening to a minimum)
Q*bert
Space Invaders, if you assign a nearby key to shoot
Q*bert's Qubes
Have fun, and I hope your hand gets better!

The Ace Attorney games can all be played with one hand, they're lots of fun.

Davideo7 : Pong is always a good one for one hand.. You can use either hand you want! It's for Atari, I think.. Good Luck!

Well there's Car Mania it's just a browser game mainly made for kids I think,if you don't mind just parking cars,it can be fun for a while,but it'll get boring kinda fast,but you can use the arrow keys on your keyboard,other than that I don't know many games that can be played with just one hand really,I guess you could also try Doom Warrior it's a pc game as well that only requires one hand to play pretty much,but easier if you have two,but the game is kinda explicit,so yeah...it's not a game for everyone,but other than that as I said earlier I don't know of that many games that require one hand. There's also Halo Wars,it can be kinda fun if you love strategy games.

Doom Warrior [is kinda explicit and requires a mature audience]  and Car Mania are pc games. Then Halo Wars it's a Xbox 360 game I don't know if it is for PC or not.

I knew of another one just I can't remember its name,someone later on might recommend it. I just know it is a strategy alien game that's kinda like halo wars.

I'm fairly sure that Breakout and Arkanoid can be played with one hand. After all, the only controls are moving left and right, so there you go!

Blendoku for mobile phone.

It's pretty much a simple (or not so simple) puzzle where you arrange the colors in a way that it blends smoothly and changes according to the given colored boxes. You seem like a person who loves and is great at designing through CSS and photoshop thus making you familiar with color palettes, so I think you'd like it.

Davideo7 : Might not be the answer your looking for but if you own a Game Boy Advance SP and any Pokemon game it's pretty easy to do, heck any turn-based rpg on a Game Boy Advance SP is manageable with one hand.


Edit: yes I'm talking about the handheld not the rgr.

Not sure if it has been recommended already but the Phone/Tablet version of DQ VIII can be played with one hand on the phone (tablet too if you can hold it in one hand) Pretty much any SRPG or TRPG and any turn-based rpg can be played with one hand, it'll just take longer to move around or select an attack. Only being able to use one hand must suck. Hope it gets better.

I would recommend the following games (they can be played with one hand) :
Disgaea:
the Disgaea series is a tactical Role-Playing game.The version for handheld game system has a different name than that for consoles like PS2/PS3.
The games are the following:
Disgaea: DS (NDS) / Afternoon of Darkness (PSP) / Hour of Darkness (PS2)
Disgaea 2: Dark Hero Days (PSP) / Cursed Memories (PS2)
Disgaea 3: Absence of Detention (PSVita) / Absence of Justice (PS3)
Disgaea Dimension 2: PS3 only
Disgaea 4: A promise revisited (PSVita) / A promise unforgotten (PS3)
Disgaea 5: Alliance of Vengeance (PS4,not yet released)

Hmm games that are easiest to play one handed. I think I will go with Role playing games for this one. My suggestions come from me having to do that at one time because my hand was in a cast and I couldn't use it . Those suggestions would be : Any of the Suikoden games, early Final Fantasy games, any  Dragon Warrior games, any Persona games, Wizardry, Destiny of An Emperor 1 & 2, any of the Shinning Force games. Could name more but I remember playing them one handed. Hope that helps ya' out. :O)

Davideo7 :
I would have suggested the Mario and Luigi: Dream Team but I just realized it needs 2 arms. Though there are the giant luigi battles that only use one hand.