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.
Probably already been mentioned,
go to an online gamesite: kongregate, armorgames, newground.
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.
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.