Alright guys, this is a suggestion thread, not one to try and further an agenda for your console of choice. If you can't add anything useful Riot I suggest just staying out of the thread.

Well no problem. But be sure to get more info about those games ;)

Edit: @Torillian: Sorry!

1. Gran Turismo 3 or 4
2. Grand Theft Auto Vice City or San Andreas
3. God of War 1 and/or 2

Those 3 or 4 games would keep you going for many weeks

Shadow of the Colossus
Shadow hearts 1 & 2
Metal Gear Solid 3
Gran Turismo 3 or 4
Resident Evil 4
Grand Theft Auto series
Final Fantasy X
God of War I and II
Devil May Cry 1 & 3
Dark Cloud 2
Kingdom Hearts 1 & 2
Disgaea 1

Devil May Cry 1 & 3 - Pretty good action games. Don't get Part 2 - it sucks. You don't have to play it to understand the story for the third game.

Silent Hill 2 & 3 - Very good horror games. They're some of the scariest games I've played. They set the mood/atmosphere perfectly, and it also tells a pretty good story, especially 2. Silent Hill 3 is a sequel to the first game, but it recalls the events that happened in the first game. The only thing that may bother you is the camera angles. Don't get Origins - it sucks. SH4 is a mixed-bag.

Onimusha series - Same as Devil May Cry. You can purchase the collection pack for around $20 online. http://www.amazon.com/Onimusha-Essentials-Playstation-2/dp/B001FBJUYK/ref=sr_1_1?ie=UTF8&s=videogames&qid=1254279839&sr=8-1

Digital Devil Saga 1 & 2 - Very good RPGs. They have a great story, and the battle system is pretty fun. Just a warning, it can get difficult. They just got reprinted, so they shouldn't cost as much as they used to. If you enjoy them, then I recommend you move on to the superior RPG - Shin Megami Tensei: Nocturne. They only reason why I recommended Digital Devil Saga instead of Nocturne is because it's more accessible to newcomers.

Yakuza 1 & 2 - very good games. You'll probably have to get them online.

Persona 4 - one of the latest and best JRPGs on the system.

Dragon Quest 8 - this game has so much heart in it!

Final Fantasy XII - Very fun to play. If you agree with the gameplay mecanics, count 200+ hours of very good entertainment.

God of War 1 & 2 - Beat it. Beat it again. You will feel the need to just do it again. Such a marvelous ride those game are!

Jak & Dexter , Jak 2 & 3 - Best platformers on PS2.

Final Fantasy X - Classic final fantasy evolution.

Metal Gear Solid 2 - Most hyped PS2 game. For me it delivered in every aspect. Story and characters are shocking and unforgettable. Have to play this to feel all MGS4 awesomeness.

The games I would highly recommend for the system are:

Dragon Quest VIII
Suikoden III
Zone of the Enders 2
Final Fantasy X
Capcom vs SNK 2

Dragon Ball Z: Tenkaichi Budokai 3

Other games I thought were really good you can look into:

Dead or Alive 2: Hardcore
Odin Sphere
Final Fantasy XII
Grand Theft Auto: Vice City
Shadow of the Colossus
Way of the Samurai
Victorious Boxers 2
X-Men Legends 1-2
Risk: Global Domination

Also check out some past PSX games. Stuff like Castlevania: Symphony of the Night, Suikoden I+II, FFVIII, Chrono Cross, Strider 2, etc.

I like your choices. Have you tried Dark Cloud 2 or Kingdom Hearts?

Unfortunatelly i hadn't played Dark Cloud 2 :( 

I played KH1 and KH2 - very good games. Great mix of characters/worlds and good story. Had such great moments with those. I recommend too. Who didn't want to see Dysney characters in a Square Enix game? :) 

RE4 is the best game on PS2, followed closely by MGS3, FFX, FFXII, DMC1 and DMC3.

Persona 4 also, if you're a Soriku-baka.

And that's the bottom line, because Stone Cold said so.