Earlier, I posted about the game ICBM, in which you do—in a very real sense—absolutely nothing. For balance, then, here's a free game in which you do something. It's called The Stranger, and it's a first-person adventure platformer in which you explore a mysterious island.
There's a talking squirrel, a triangle-headed guy, and lots of things to discover. More importantly, there's a grappling hook device that lets you grab onto specific parts of the environment.
Really, though, the reason to play is the The Stranger's atmosphere. First-person exploration games can be very self-serious, but here it's just sort of... nice. Take a look at the trailer to see what I mean.