Shit, this is really hard for me, since I've started to realize I have far too many favourite games...
But I'm afraid I'll have to say Grim Fandango - It's just so goddamn good... Can't explain it... The storytelling, the characters, the music, the graphics, the voices... You want me to mention more stuff I love about it?
Others that come close are of course GK1, DoTT, MI2 and Discworld Noir.
All of these games have something important in common - They all had an atmosphere that drew me in, and made me longing for more when the game was over. Not every game does that to me. GF was the one that had the biggest influence, though - And therefore it deserves the #1 spot.