Given that most of the free games available are MMOs...
World of Tanks
And if you really hate yourself, Maplestory. Somehow, this Korean grindfest monstrosity is still alive. But what it does right is that the cash shop is pretty much cosmetic only, unless you're playing certain classes. Don't play this if you don't want to piss away months of your life, though.
The Human Instrumentality Committee: An Evangelion Fan Group
Steam name: Baron Von Kittenkiller
Xbox Live Gamertag: CrisisRain
League of Legends IGN: NoOneLovesYou
Skype username: tehlawgiver
Probably already been mentioned,
Sig created by Vanquished
Stars of Eden
go to an online gamesite: kongregate, armorgames, newground.
Credit to Harby the Australian Harbringer.
Get Black Mesa, a remake of the original Half Life. It has the same graphics and engine that Half Life 2 does, and it's totally free.
I don't know what to put here right now.
If you're feeling like a mixture of Minecraft, Sim City, and an economics class, try Dwarf Fortress. I'd suggest reading the Quickstart Wiki and grabbing a texture pack if you're interested.