Wow, someone already mentioned Adventures of Cookie & Cream, my favorite PS2 game. So I'll say it again: try this game!!!

def. play Kingdom hearts 1&2, Ico, and Dark Cloud 2. I also hear that Rouge Galaxy, Persona 3(maybe be M rated actually), and Odin's Sphere are really good.

Final Fantasy 10 & 12, Prince Of Persia: The Sands of Time, Warrior Within & The Two Thrones.

does anyone else think kingdom hearts is a bit overrated? i have the first one and played through at least over half of it back when it came out and while the story and the whole idea of the game was really cool and all the different places to go were awesome the actually fighting wasn't very good. pretty much the only bad guys are the shadow creatures or whatever and they only come in a few varieties and it basically comes down to a hack n slash fighting style without much strategy and no variety. everything else about the game was awesome but because of that i always thought of it as good but not great. anyway i'll just add that half-life is on ps2 so that'd be a good pick up. ah but i guess that is M. so i got nothing beyond what other people said.

Let's look at how good the Playstation 2 games really are, without any M-rated games, sports games, driving games, and games that got less than 80% on Game Rankings...

E + E10+ rated games

Jak and Daxter: The Precursor Legacy
Sly 2: Band of Thieves
Rayman 2 Revolution
Sly Cooper and the Thievius Raccoonus
Klonoa 2: Lunatea's Veil
Mega Man Anniversary Collection
Rez
Ape Escape 2
Rayman 3: Hoodlum Havoc
We Love Katamari
DDRMAX: Dance Dance Revolution
Katamari Damacy
Karaoke Revolution Volume 3
Frequency
Karaoke Revolution
EyeToy: Play
DDRMAX2 Dance Dance Revolution
Gitaroo Man
Karaoke Revolution Volume 2
Kingdom Hearts
Ace Combat 04: Shattered Skies
Theme Park Roller Coaster
2. Kingdom Hearts II
5. Lego Star Wars II: The Original Trilogy
7. Sly 3: Honor Among Thieves
9. Karaoke Revolution Party

If you're only looking for good E, or E10+ games, you wont find much too much on the Playstation 2.

T-rated games

Ratchet & Clank: Up Your Arsenal
TimeSplitters 2
Virtua Fighter 4: Evolution
Soul Calibur II
Virtua Fighter 4
Ratchet & Clank: Going Commando
Ratchet & Clank
Tekken 5
Jak II
Viewtiful Joe
Medal of Honor Frontline
DOA2: Hardcore
Soul Calibur III
Guilty Gear X2
Psychonauts
WWE SmackDown! Here Comes the Pain
Tekken Tag Tournament
Jak 3
Maximo: Ghosts to Glory
The Lord of the Rings: The Return of the King
James Bond 007: Everything or Nothing
Star Wars: Battlefront II
WWE SmackDown! vs. RAW 2006
Viewtiful Joe 2
Freedom Fighters
WWE SmackDown! Shut Your Mouth
TimeSplitters
The Lord of the Rings: The Two Towers
Ratchet: Deadlocked
Maximo vs. Army of Zin
Call of Duty 3
Gradius V
Star Wars: Battlefront
Capcom vs. SNK 2: Mark of the Millennium 2001
Tekken 4
Time Crisis 3
James Bond 007: NightFire
Alien Hominid
Battlefield 2: Modern Combat
WWE SmackDown! vs. Raw
MDK2 Armageddon
Def Jam Vendetta
Street Fighter Alpha Anthology
Project: Snowblind
Metal Arms: Glitch in the System
Okami
Prince of Persia: The Sands of Time
Shadow of the Colossus
ICO
Tom Clancy's Splinter Cell
Bully
Beyond Good & Evil
Tom Clancy's Splinter Cell Pandora Tomorrow
The Incredible Hulk: Ultimate Destruction
Mercenaries
Rygar: The Legendary Adventure
Peter Jackson's King Kong: The Official Game of the Movie
Tomb Raider: Legend
Fatal Frame
Tomb Raider: Anniversary
Spider-Man 2
Escape from Monkey Island
Guitar Hero II
Guitar Hero
Guitar Hero III: Legends of Rock
Amplitude
The Sims Bustin' Out
Metal Slug Anthology
Sega Genesis Collection
Culdcept
The Sims
Space Channel 5 Special Edition
Final Fantasy X
Final Fantasy XII
Dragon Quest VIII: Journey of the Cursed King
Dark Cloud 2
Final Fantasy XI: Treasures of Aht Urhgan
Suikoden III
Final Fantasy X-2
Shadow Hearts: Covenant
Champions of Norrath
Final Fantasy XI
Disgaea 2: Cursed Memories
Valkyrie Profile 2: Silmeria
Baldur's Gate: Dark Alliance
Xenosaga Episode I: Der Wille zur Macht
Rogue Galaxy
Xenosaga Episode III: Also Sprach Zarathustra
Odin Sphere
Marvel: Ultimate Alliance
X-Men Legends
X-Men Legends II: Rise of Apocalypse
Star Ocean: Till the End of Time
Baldur's Gate: Dark Alliance II
Star Wars Starfighter
Ace Combat 5: The Unsung War
Star Wars: Jedi Starfighter
Robot Alchemic Drive
Disgaea: Hour of Darkness
Phantom Brave
La Pucelle: Tactics

There are far more T-rated games, than E, and E10+ rated games, combined. Even without the sports, driving, M rated, and games, less than 80%, on Game Rankings, there are a lot of Playstation 2 games to choose from. However, you can further narrow down the titles, by excluding more crap, like WWF games, and such. At the end, there should be at least 30-40 solid titles to choose from.

I'd waited with Okami to get the Wii version. The game is amazing and I've completed it but still I can't wait to play it on Wii.

Kingdom Hearts 1+2
Final Fantasy 10 (I didn't like 12)
Dragon Quest 8
Shadow of the Colossus
ICO
Beyond Good & Evil
Metal Gear Solid

Here are superb PS2 titles:

Burnout 3 and 4
Colin McRae Rally (all)
Dead or Alive 2 Hardcore
FIFA Football (the best was the 2005)
Gran Turismo (the best was the 3 A Spec)
Grand Theft Auto (all)
Guitar Hero (all)
Midnight Club (the best was the 3 Dub Edition Remix)
Moto GP (all)
MX vs ATV Unleashed
Need For Speed (the best was the Hot Pursuit 2)
Pro Evolution Soccer (all)
Soulcalibur (both)
Splashdown
SSX (all)
Super Monkey Ball (both)
Test Drive (the best was the Unlimited)
The Getaway (both)
This Is Football (all)
TOCA Race Driver (all)
Tony Hawk's Pro Skater (the best was the 3)
Twisted Metal: Black
Virtua Fighter 4 Evolution
Virtua Tennis 2

 Yeah, I wish I could have waited for Okami but I bought it before the Wii version was announced