Silent Hill 2: Oh my god this game is absolutely glorious. BGE, GOTY any year, etc... Play it.
Final Fantasy VI/VII/X: Well, it's Final Fantasy
The Last Of Us: I've just never seen a game with such a strong story and strong characters. Never. And I love narrative games. This game is simply legendary.
Halo 2: Because holy hell it's epic. And the graphics at the time, my god...
Mass Effect: I love Sci-Fi, and I love Bioware. Of course I love these games.
Dragon Age Origins: Remember when I said I loved Bioware ?
Asura's Wrath: I know, I know... This one is a guilty pleasure. I was just SO into the game at one point, it was just great. I loved it.
Pokémon Gold/Silver: The first Pokémon games I owned. The very first games I owned actually.
There are a lot of other games that I love, but these are my absolute favourite.