Surprising that none has mentioned Path of Exile.
Path of Exile is an online action RPG. You can play it alone, although there is a PvP option. There is a little shop as well, but that's mostly cosmetic things. Complete optional.
PoE is made by Griding Gear Games. It's set in the world of Wraeclast, a dark and unwelcoming region. You can choose from six classes and there is also a seventh one (but that one is unlocked near the end)
PoE is a free 2 play game. http://www.pathofexile.com/
An other indie of note is Legend of Grimrock, which is a dungeon crawler.
It's made by Almost Human. http://www.grimrock.net/
A sequel seems to be coming. Legend of Grimrock is avalable on Steam and on Good Old Games.
For those who like survival horror games, try Amnesia: The Dark Descent from Frictional Games.http://www.amnesiagame.com/#main
There is also a sequel now called Amnesia: A machine for pigs. Frictional Games are also the ones behind Dear Esther.