Oh man that's hard to decide. My honest answer has to be Batman: Arkham Asylum. I was still on a Batman high after The Dark Knight, so the thought of having a Batman video game with the same voice cast as Batman: The Animated Series had me hyped as hell. I was sold just 5 minutes in. I knew I was in for a special ride. From seeing the interactions between Batman and Joker like it was the 90s animated show again, to using the detective skills, to the psychedelic trip of the Scarecrow level that made you think your game crashed, all being seen through an addicting combat system, stellar music, and an atmosphere that truly made you feel like you were in the Arkham Asylum from the comic books. Everything was just so perfectly made.
What I would give to experience it again for the first time.
Other notable games that also come to mind would be Halo: Combat Evolved, Pokémon Red/Blue, StarCraft, Warcraft 3, WipeOut XL, Vanilla WoW, Half-Life 2, Jet Set Radio Future, and Call of Duty: Modern Warfare (the opening ship level had me feeling like I was watching a Hollywood action movie)
You called down the thunder, now reap the whirlwind