Friend of mine can only use one hand, need a list of fun mouse only games.

yu gi oh!

I have problems with my own left hand, though not so bad that a gamepad is unusable. Hope he improves soon.

Look at some RPGs you can play with the mouse like Shadowrun Returns.

Would non Steam games be acceptable?

Blue Toad Murder Files is part of the Blink Bundle. Also, I enjoyed To The Moon, kind of a story driven point and click game. He may also enjoy "Time Gentlemen, Please!" and "Ben There, Dan That!". Also point and click, but the controls are a little weird to get used to.

Edit: ALSO! Been a while, but I think that "Don't starve" is mainly mouse driven, as well as "Octodad: Dadliest Catch" (though you can play with keyboard)

To The Moon, if he is interested in a great story!

I can help with civ iv

Scratches: Director's Cut can be played with one hand. Syberia can be played with a mouse, too - you only use ESC to skip cutscenes and save/load.

At the top of my head:
Audiosurf 2
Puzzle quest
Race the sun
10,000,000
McPixel
Any telltale games (I think so)
Fieldrunners 1 or 2
Any game here except gone home

Faerie Solitaire, Syberia 1&2 and puzzle kingdoms are good with a mouse. Would recommend Ceville, Nightmares from the deep : The Cursed Heart (or any by the makers of this), Legend of Fae.
Possible Magic the gathering 2012, 2013 or 2014, The Kings Bounty Series, Might and Magic Series.

X-com can be played mouse only, it's a turn based action-shooter against aliens. The base game is amazing(and hard), the DLCs are worthy.
As for your maybes: Faery solitare is a card game, nothing special, an OK game. I've played Syberia 1&2 thoose are OK too, point and click adventure games.
What I would suggest you is Civ 5, I think it was in a pervious bundle also, even the base game is very fun, challenging, and kinda unlimited replayability.

Heroes of Might and Magic 3.

Audiosurf
Hero Academy
Papers Please
Super Hexagon
To the Moon

From your maybe list faerie solitaire, the 39 steps and hero of the kingdom are all playable mouse only

Neighbours From Hell.

Hero of the Kingdom

Defense Grid is a good mouse only game

Hearthstone (not-steam, blizzard's game, free to play, 100% mouse, card game, so much fun)

You can check this game 5 days later, dunno if it is playable with one hand keyboard. But it looks so much fun, I'm waiting for release to buy.

I think tycoon games are playable with only mouse (like city xl, simcity, roller coaster tycoon 3 -so fun-) too bad i gifted Cities in Motion 2 to my friend :/

Super Hexagon from your list is playable with 2 buttons only, so one hand :)

McPixel from your list is playable with only mouse, but worst game (is it even a game) I've ever played

I'm not sure if limbo is playable with one hand keyboard? If it is possible i can gift

BTW will he/she get better? Is he/she going for physiotherapy?

Cthulhu Saves The World is a fun retro-RPG with turn based battles

it's not mouse-only, but it can easily be played with 1 hand on the keyboard, no need for mouse input.

Spacebase DF-9

Fallout 1&2

FTL= mouse + Space(sometimes)

Unholy heights is a cute and fun tower defense game, and you can buy it for $4!
Also, I recommend Deponia series.

When I broke my arm last year I played Dragon age: Origins. While battle you can use mouse only and after it you can move using mouse or WASD only. So one hand is enough for this game =)

How about Broken Sword series?

Someone had a similar question I guess it can help you. :) Link

Civ is purely mouse driven, excellent choice. Extremely high replay value due to the gazillions of ways the games can play out due to options and choices. While it's not on Steam, D2, or any of the better Diablo clones can be played purely via mouse. Torchlight is pretty decent, iirc only would need occasional, low intensity key presses to do things like open the inventory...may even have click options.