I love games that somehow just do an amazing job of invoking my emotions. They do it better than many movies in some cases.

For that, my favorite games are Legend of Mana (I still hate ending the game), Legend of Zelda: Twilight Princess (Zant's chuckle just gives me the creeps), and Okami (didn't buy it, but rented it enough that I could've. I'm getting it for the Wii).

The Myst series for computer does a lot of that as well. Especially the third installment.