Disgaea 2
God Hand
God Of War
Metal Gear Solid 3
Metal Gear Solid 2
Def Jam Fight for NY.(Maybe)

I cna't really remember anything else.

This should be a forum post. As for the question, I can't choose 10. It's too hard to remember and too hard to choose what I do remember.

I guess I'd keep:

Metal Gear Solid 2 and 3

Final Fantasy X

Ratchet and Clank: Up Your Arsenal

GTA: San Andreas

God of War 1 and 2

And that's all I can remember right now.

Looking at my shelf here, i'd say:
Jak and Daxter
Star Wars: Battlefront 2
Devil May Cry
FFX
GTA (3 or San Andreas)
God of War 1 and 2
Kingdom Hearts (the first)
Mercanaries
MGS:3
Ratchet And Clank (Any)

Super Dimensional Fortress Macross
Okami
Odin Sphere
The Warriors
Beyond Good & Evil
ICO
Shadow Of The Colossus
Guilty Gear XX
Transformers (not the movie game)
Zone Of The Enders 1 & 2
Front Mission 4 & 5
God Hand

STEAMBOT CHRONICLES

A good PS2 collection needs to have

-GTA 3/Vice City/ San Andreas
-God of War
-Burnout 3/Revenge
-MGS 2 & 3 (And, not or)
-Katamari Damacy
-a JRPG of your choosing
-SSX 1/3 (Not Tricky)
-Shadow of the Colossus/ ICO
-DMC 1/3
-Jak & Daxter/Ratchet & Clank/Sly Cooper

Come to think of it, this list is really dependent on your needs. It skews a bit heavy towards action/adventure/platforming action, but feel free to add Gran Turismo, Ridge Racer, etc. etc. for your racing needs, or Kingdom Hearts, Shin Megumi Tensei, and beef up the JRPG selection. Hell, I totally disregarded Survival horror- not my scene, but an "essentials" pack should probably have some Silent Hill, or Fatal Frame. And Fighting games, too. Tekken/Soul Caliber/ Virtua Fighter...

Making a "definitive" list is a real hassle with the PS2.

A list highlighting the, er, highlights of the PS2 should probably have-

GTA ( I think this can be agreed upon)
1 Fighting Game (I'll go with Soul Calibur)
2 Racing (Burnout for the glorious arcadey goodness, Gran Turismo for boring ultra realism)
1 RPG (I'll pick FFX, just for the easy answer)
1 Sports game (Madden, NBA Street, Tony Hawk- pick your poison. This one really is up in the air. I'll go Tony Hawk)
1 FPS (I'll go with MoH: Frontline, for getting the whole package right before it became a cliche)
1 Party Game (Like it or not, the PS2 might have been the casual gaming seed. Singstar, the Eyetoy, that stupid quiz game with the four game show looking controllers... And my choice, that one with the guitar)
1 Action Adventure (Here's where blood get spilled. Does God of War beat ICO? Is Metal Gear Solid more fun than Splinter Cell? (and should they be in the shooter category?) Is Jak's platforming > Ratchet's shooting > Sly's sneaking? (Another sneaking game. Hmm, maybe there should be a Stealth game category.) Should the LotR games get the nod for being some of the best licensed material games ever? This category should probably be pushed up to two, and Burnout should be the only racing game, but it's my list and I get to make those arbitrary kind of decisions.)
1 Katamari (I don't think there is any contention for this spot)

I was going to come in here and say SHADOW OF THE COLOSSUS!!! But I see it's under control.

Everyone seems to have covered everything. Hmmmm...

KOF XI
KOF 2006
Disaster Report
Cold Winter
Killzone
Magna Carta
Onimusha series
Persona 3
Shadow Hearts series
Shadow of Rome
Silent Hill 2 & 3
SOCOM series
Suikoden series

Hmmm.. apparently "every time" is not one word.

I have shamed myself.

My dog won't stop farting, it's awful.

lol @ Rorscach. Finally.

Metal Gear Solid 2: Substance
Metal Gear Solid 3: Subsistence
God of War
God of War 2
Shadow of Colossus
Devil May Cry
Silent Hill 2
Indigo Prophecy
Killzone
Resident Evil 4

Those are my favorite PS2 games, mind you Indigo Prophecy I think plays better on Xbox.