Two GameCube games I'd like to add are Eternal Darkness: Sanity's Requiem and Doshin the Giant. You probably will not find two games who are more different, though...
Anyways.
Eternal Darkness is a very atmospheric and masterfully told tale of Lovecraftian horrors, and has one of the best concepts in any game ever; the sanity meter. Basically, the more horrible things you see, the madder you get, and the game starts to behave rather bizarrely.
Doshin the Giant is a game in which you are a big yellow giant who wanders around lazily, helping or killing and maiming little villagers who will build monuments to honour or disgrace you. The game's a little obscure, maybe, but I like to pop it in occasionally.
I would also like to add the Metal Gear Solid series. It does get a lot of flak for writing that is, in some places, more than a little bit overdone. But;
The first game has some excellent scenes (Cyborg Ninja or Psycho Mantis, for instance) and the plot was solid (heh).
In the second game, I really like the parts when the AI starts messing with the head of the main character and you. "Fission Mailed", anyone? I need scissors! 61!
The third game has three parts in particular that struck me as wonderfully "artsy". The first is the boss fight (so-to-speak) against the Sorrow, wherein you wade through a river against a stream of all the people you have killed. The other is the fight against the End, who is a camouflaged sniper geezer. Finally, the fight against the Boss in a field of white flowers is executed very well.
The fourth game doesn't have quite as many "artsy" qualities. It is more or less a celebration of the preceding games. If you are inclined to be nice to it, that is. If not, it could be described as a ferocious self-wank. Though one could argue that the artistic value of the game lies in the attention to detail put in to almost everything in the game. From weapons to environments.
Finally, I want to add the Oddworld games. I can't describe them in any way that makes them justice. Just go and play them!