Good Playstation 2 games...

[L9OBL]

GoW 1 & 2
Jak series (Jak and daxter, jak 2 Jak 3)
Ratchet and clank series
sly cooper series
ico series (ico, shadow of the collosus)
PoP series (ps2 ones were good the new one (ps3) sucks though)
Okami

those are probly the best games ever

 

[j0z]

Jak series (But not Jak Racing if you have a PS2 Slim, compatibility issues)
Ratchet and Clank series (3 was best, then 4, then 2, then 1)
God of War
Sly Cooper
Shadow of the Colossus
Okami
GTA 3 and San Andreas

 

[superdance14]

Every single Sly Cooper game. Play them twice. They are amazing.

 

[Nutcase]

Virtua Fighter 4 Evolution
Contra: Shattered Soldier

 

[Quaidis]

To better detail Ratchet and Clank, try to collect them in order. R&C, Going Commando, Up Your Arsenal. Deadlocked is the fourth and by far the easiest to find, but it was not all that good. They took a great platforming game and kind of made it into a strict arena fighter with less weapons to play with. Two new R&C games were ported from the PSP to the PS2: Size Matters and Secret Agent Clank. Both are okay. Size Matters is actually better on the PS2 than its hand-held counterpart.

Way of the Samurai is a good game. I enjoyed the first far more than the second, simply because you could pretty much do whatever you wanted in the first. In the second you were given too many places to go and were expected to get jobs.

Guilty Gear X was a nice fighter, though the sequels gave my thumb blisters.

And if you want to collect some RPGs (though there are many better rpgs for the PS1), look out for the first game in the .Hack series (which I forgot the name of), Arc the Lad: Twilight of the Spirits/3, Star Ocean: Til the End of Time, the two WildArms PS2 games (3 and a remake of 1), the two DarkCloud games, Tales of the Abyss, FF12, and Grandia 2.

 

[Hazy]

GTA 3, VC, and San Andreas
Shadow of the Colossus
God of War 1+2
Persona 3

 

[Troublesome Lagomorph]

God of War, Gta series, Shadow of the Colossus would be my picks. I also heard Ico was good.

 

[dragonburner]

Single Player:
God of War 1 and 2
Shadow of the Colossus
Ico
The Ratchet and Clank series (My favorite is Up Your Arsenal but...)
Sly Cooper 1, 2, and 3
GTA

Multiplayer:
I like the Star Wars Battlefront series a lot so that is my suggestion

 

[Mischiviktus]

Jak and Daxter, Ratchet and Clank, God of War, Timesplitters: Future Perfect, there's tons of great games.

 

[squid5580]

oden sphere
grim grimoir (best story ever)

Odin sphere is pretty but laggy and very repetative (you are in a small world which you have to repeat with 5 different characters)

Grim Grimoire is very pretty and fairly innovative.

Although you can't go wrong with Ratchet and Clank.

 

[Rigs83]

Bushido Blade
It is actually a PS1 game but no fighting game like it has come out in my memory.

 

[Tartarga]

i recommend a series of jrpgs called .Hack G.U. its a hack and slasher but it has beautiful scenery which you could stare at for hours also there are some pretty interesting boss fights but if your not a fan of jrpgs then don't play them

 

[ConnorCool]

the GTA's, God of war 1+2, destroy all humans, tony haks, american wasteland

my fave PS2 games tbh

 

[lostclause]

It's already be said but SW Battle front two is good. I've clocked up a ridiculous number of hours on that game (albeit on xbox), huge replay value. Also if you're looking for fps's 40K, Fire Warrior is worth a look. It's not brilliant but it's fairly good.