In no particular order:
1.Planescape: Torment in terms of writing
2.The Thief series for immersion
3.Fallout series, excepting Tactics, for that feeling of morbose wonder. Tactics is a good game, but barely any writing (BOS doesn't exist, got it?)
4.Super Castlevania IV for sheer awesomeness, and the fact that it represents my early years.
5.Max Payne for solid gameplay, interesting delivery and pretty decent length, which most action games lack nowadays.
6.I agree on Psychonauts, I laughed my ass off. I played it two times in a row for the dialogues alone!
These are actually from the ones in my collection, it'd be too difficult for me to choose from ALL games, when I don't really know them.