I would nominate the free-to-play web-game "Today I Die" (google it, I don't think I'm allowed links here). Like many others, I could argue for "Shadow of the Colossus", "Flower", "Ico" and even to a certain extent "Bioshock" (though I actually think the art of Bioshock is too divorced from the actual game), and of the nominees we can vote on here "the Longest Journey" is the one that touched me the most.
However, "Today I Die" is the first instance I've come across of a successful "game as poem". It actually brought a tear to my eye, and I immediately showed it to my girlfriend who had the same response. It's only 10 minutes of your life, but it is undoubtedly art in a way that could only be expressed as a game.
Edit: Hell, I'll post a link anyway, you guys really need to try this:
http://www.ludomancy.com/games/today.php