Final Fantasy VII - A truly amazing game that proves you don't need lifelike graphics to tell a genuinely emotional and impacting story; in my opinion, it is one of, if not the most incredible fantasy epic ever told.
Shadow of the Colossus - An incredibly atmospheric and beautiful game, unique and epic beyond imagination. Also, the use of interactivity at the end is truly amazing and makes for an incredibly emotional ending.
Beyond Good and Evil - A quirky sci-fi adventure with great variety of well-executed gameplay styles and an awesome story. Great characters, great music, great atmosphere... this game is a masterpiece.
Mass Effect 2 - Taking interactivity to a new level by basing itself off the player's choices in the first game, Mass Effect 2's main story and RPG elements were a little weak, but the cast of characters and level of player interaction with the story makes it one of the best interactive experiences out there.
Halo: Combat Evolved - This game revolutionized console shooters, and though it gets a lot of hate now for inspiring unoriginality in the genre (everyone copied it, so that must mean it sucks... right?), it is truly an amazing game. Revolutionary mechanics meet intricately designed atmosphere and a great sci-fi war story, aided by one of gaming's greatest soundtracks.
Runners Up:
The World Ends With You
Okami
Mass Effect
Bioshock
Prince of Persia: The Sands of Time
Fatal Frame
Fatal Frame 2: Crimson Butterfly
Phoenix Wright: Ace Attorney
Final Fantasy VI
Final Fantasy X
Crash Bandicoot Warped
Chrono Trigger
Metroid Fusion
Elite Beat Agents
Portal
Portal 2