Best of the PS2 era

I want bad rats for PS2.

You may enjoy Okami. Great fucking game, piece of art. The soundtrack alone is very good.

metal gear solid 2 and 3, must play games for ps2!

Time Splitters 3

The God of War games, the DBZ Budokai games, the Metal Slug games, GTA games, and the ones you mentioned as well

Give me some time. I've owned hundreds of PS2 games over the years. I'll edit this post with a kick arse list.

Amplitude
Ape Escape 2 / Ape Escape 3
Arc the Lad: Twilight of the Spirits
Baldur's Gate: Dark Alliance II
Burnout 2: Point of Impact / Burnout 3: Takedown / Burnout Revenge / Burnout Dominator
Capcom vs. SNK 2: Mark of the Millennium 2001
Castle Shikigami 2
Champions of Norrath
Devil Kings
Devil May Cry 3: Dante's Awakening Special Edition
Dog's Life
Downhill Domination
Drakan: The Ancients' Gates
Fatal Frame / Fatal Frame II: Crimson Butterfly / Fatal Frame III: The Tormented
Freedom Fighters
Genji: Dawn of the Samurai
Ghosthunter
Gitaroo Man
God Hand
Guilty Gear XX Accent Core Plus
Haunting Ground
ICO
Katamari Damacy / We Love Katamari
Killer7
King of Fighters XI, The
Klonoa 2: Lunatea's Veil
Makai Kingdom: Chronicles of the Sacred Tome
Maximo vs Army of Zin
Obscure
Okami
OutRun 2006: Coast 2 Coast
Phantom Brave
Punisher, The
R-Type Final
Ratchet & Clank / Ratchet & Clank: Going Commando / Ratchet & Clank: Up Your Arsenal / Ratchet: Deadlocked
Red Star, The
Rez
Second Sight
Shadow Hearts / Shadow Hearts: Covenant
Shin Megami Tensei: Digital Devil Saga
Shin Megami Tensei: Nocturne
Shinobi
Sky Odyssey
Soul Nomad & the World Eaters
Steambot Chronicles
Tenchu: Wrath of Heaven
TimeSplitters / TimeSplitters 2 / TimeSplitters: Future Perfect
Urban Chaos: Riot Response
Virtua Fighter 4: Evolution
Warriors Orochi
Way of the Samurai
Ys: The Ark of Napishtim
Zone of the Enders: The 2nd Runner

I haven't listed every great title, but with a library of thousands, there is too much to pick from.

Shadow of the Colossus, not really comparable to any other PS2 game, but you should give it a try if you can get it somewhere. Also Ico, didn't play it but seems to be awesome. if you own a PS3 you should get the HD-Remake Double Pack, it's even cheaper than the the original games.

Star Wars Battlefront 2

If someone likes JRPG-s/tactial RPG-s (and has a lots of free time):

Digital Devil Saga 1-2
Lucifer's Call/Nocturne
Persona 3-4
Xenosaga 1-3
Shadow Hearts 1-3
Final Fantasy series
Wild Arms 3-5
Suikoden 3-5
Disgaea 1-2
La Pucelle
Phantom Brave
Rogue Galaxy
Tales series
Ar Tonelico 1-2
Atelier Iris 1-3
Mana Khemia
.dot HACK series
Dragon Quest VIII
and so on

GTA: SA?

Vice City!! :)

/v/ has a recommended list

But my suggestions are
Devil May Cry 1 & 3
.hack://Infection, Mutation, Outbreak, and Quarantine - If you stand the combat you'll find yourself a great series of games. Ignore anything else .hack// related like .hack//G.U. It's pure condensed shit
God Hand
DragonBall Z: Budokai 3 - I don't care what anyone says this one of the most funnest fighting games I've played and I dislike DBZ.

Kingdom Hearts dialogue isn't it's strongest point, it's more just the fact that you can visit all those Disney worlds + Final Fantasy cameos. I enjoyed them though, soundtrack was good, loved Gummi Ships (especially in KH2).

As for other PS2 games...
Gran Turismo 4
Ratchet & Clank series
Dragon Ball Z: Budokai Tenkaichi series

I didn't own many PS2 games, they were pretty expensive back then for me.

Tony hawk Series, GTA Vice City Stories, Black, Burnout series.

Kingdom Hearts, Dynasty Warriors games, Ghosthunter,etc

Want an RPG that was sadly overlooked, and is an amazing piece of gaming? Rogue Galaxy. My highest reccomendation for all the PS2 era RPG's, amazing cel art look. The studio that made it, Level 5, is also known for making Dark Cloud series on ps2, as well as the more recent White Knight Chronicles games and the critically lauded Ni No Kuni: Wrath of the White Witch.

edit: see a lot of others mentioned this just before me, glad to see not everyone overlooked it. The game is incredible, and really must be played.

PS2 games I had most fun with:
Gran Turismo 3, 4
Ratchet & Clank 2
Jak & Daxter
Tekken Tag Tournament
Soul Calibur 3
Dynasty Warriors 5
Metal Gear Solid 2 and 3
Dragon Ball Z Budokai Tenkaichi 3
Beyond Good & Evil
Pro Evolution Soccer
Dead or Alive 2

Some good games from PS2 era I played on different platforms, but they were released on PS2 too:
Guilty Gear XX series
Metal Slug series
Resident Evil 4
Persona 3
Katamari series

And I still have many games I bought but didn't finish yet, like Devil May Cry series, Kingdom Hearts or Marvel vs Capcom 2. PS2 had maaaany great games, and it lived, in my opinion, during greatest era for video games. Era, where games weren't so expensive to make and developers experimented with them much more than nowadays, making enormous variety of games.

Silent Hill 2.

and FFX + Kingdom Hearts.

Shin Megami Tensei Persona 4.
Best game ever.

Anybody played Fahrenheit?
Awesome game

Gauntlet: Dark Legacy
Champions of Norrath 1 & 2
Megaman X: Command Mission

Crash Bandicoot!
I hope I don't need to explain why :D
Still wondering how could it be people didn't mention it here...
Also, The Legend of Spyro: Dawn of the Dragon was awesome! At the beginning, I didn't like this new idea for Spyro games, although this one is really good and I enjoyed it very much. A lot of fun, especially while playing coop mode (I ended the whole game with my sister). I also loved upgrading system. It was so fun when me and my sister were choosing and giving advices to each other what skill should we upgrade etc. :D The only sad part is that the game is rather short:( Can't recall other great games for now if but I did, I'd come back here for sure.

.> no one mentioned the SSX series... what a shame

Disgaia 2 and Makai Kingdom, Suikoden 5 (and 4 to a lesser degree), Mana Khemia : Alchemist of Al Revis and too many to count.

Ratchet and Clank series!