Garcian's Annotated PS2 Must-Have List:
EXCLUSIVES
Devil May Cry 1 & 3: Very good beat 'em ups. Skip 2.
Dragon Quest VIII: If you like oldschool console dungeon-crawlers, this is the game for you.
God of War 1 & 2: Cinematic-style action games. Some of the best out there.
ICO: A short, Prince of Persia-style action/puzzle game, notable for its excellent use of atmosphere.
Katamari Damacy & We Love Katamari: One of the best pick-up-and-play games I've ever played.
Metal Gear Solid 2: Over-the-top stealth action. Skip the codec conversations if you want.
Odin Sphere: A beautiful 2D beat 'em up with RPG elements. You'll either love it or hate it, but you need to give it a try.
Ratchet & Clank series: Fun shooter/platformers.
Shadow Hearts 1 & 2: RPGs with a fun battle system and a bizarre sense of humor. Skip From The New World.
Shin Megami Tensei series: The best RPGs for the system. There's five of them for the PS2, and all are worth playing, though Nocturne and Persona 3 most of all.
Sly Cooper series: Good platformers with some stealth thrown in.
Soul Reaver 2: Action game with a kick-ass story. Best played after playing the first two games in the series, so you understand what's going on.
Tales of the Abyss: Real-time-battle RPG that's also the best Tales game out there.
MULTIPLATFORM (Play these on other systems if you can, since the PS2 versions are usually graphically inferior)
Beyond Good & Evil: A great "Zelda-like" with stealth elements by the creator of Rayman.
Killer7: An artsy, post-modern rail shooter, odd as it sounds. One of my favorite games.
Legacy of Kain Defiance: The last game in the LoK series, so play the others beforehand.
Max Payne 1 & 2: Over-the-top third-person shooters with BULLET TIME.
Prince of Persia series: Action/puzzle games that are really hard to beat in quality.
Rayman 2 & 3: Amazing 3D platformers.
Second Sight: A supernatural shooter where your character has a lot of awesome powers; by Free Radical (the Timesplitters guys).
Silent Hill series: The best horror games out there.
The Suffering: A horror-shooter that's either first or third person, depending upon your preference. Skip the sequel.
Viewtiful Joe 1 & 2: Old-school-style 2D beat 'em ups.
The Warriors: Brutal beat 'em up based off of the movie of the same name. By Rockstar (makers of GTA).
"'Casual games' are something the 'Game Industry' invented to explain away the Wii success instead of actually listening or looking at what Nintendo did. There is no 'casual strategy' from Nintendo. 'Accessible strategy', yes, but ‘casual gamers’ is just the 'Game Industry''s polite way of saying what they feel: 'retarded gamers'."
-Sean Malstrom