My personal favorites include Shadow of the Colossus, Kingdom Hearts, and Zone of the Enders: The 2nd Runner.

Shadow of the Colossus, Gran Turismo 3 & 4, GTA III, Vice City & San Andreas, Prince of Persia - Sands of Time.

Lots of Shadow of the Colossus love in here. I can dig it.
 
My picks: Shadow of the Colossus, Persona 3 & 4, Metal Gear Solid 2 & 3, and the Ratchet and Clank series.

Need for Speed Hot Pursuit 2, Persona 3 & 4, SMT: Devil Summoner 2, GTA vice city

" @emem: Prince of Persia: The Sand of Time was an awesome game. "

" Lots of Shadow of the Colossus love in here. I can dig it.

Jak 3, Ratchet and Clank 2 and Vice City.

Final Fantasy 10 & 12
Kingdom Hearts 1 & 2
GTA trilogy
God of War 1& 2
and of course Shadow o the Colossus

Silent Hill 2, hands down.

God Hand, Project Zero II: Crimson Butterfly, Shin Megami Tensei: Persona 4, Guilty Gear XX #Reload: The Midnight Carnival and The King of Fighters XI are my favourites.

honestly, there aren't a ton of ps2 games that i would go back and play, other than ico and shadow of the colossus. that is, unless you count stuff like splinter cell, prince of persia, psychonauts and beyond good and evil. but i played all of those games on xbox and gamecube, not ps2.

Devil May Cry 3, Silent Hill 2, Z.O.E 2 :Second Runner, Metal Gear Solid 3: Snake Eater Star Ocean: Till the end of time, Project Zero 2, Need for Speed: Most Wanted.
 
I've never played Shadow of the Colossus unfortunately. Sounds like I missed a classic there.

Tekken Tag and 5, We ♥ Katamari, Okami, Shadow of the Colossus

Well I guess count me in also with Shadow of the Colossus. 
 
as for the others I guess Shinobi, the 1st Devil May Cry and the 3rd, Gran Turismo 3, and of course Silent Hill 2 & 3. 
 
Well Shinobi and Devil May Cry 3 was short lived when Ninja Gaiden released in 2004 which compelled me to buy an Xbox for that game alone. :p 

Persona 3, Nocturne, and the Metal Gear Solid Series.

RE4 
DMC3 
Drakengard 
Metal Gear Solid 3: Snake Eater

Vice City & San Andreas, MGS3: Snake Eater and God of War 1.
 
Honourable mentions, MGS2, Shadow of the Colossus and Burnout Takedown.

The GTAs and the Jaks.
 
...with an honourable mention to SotC.

Shadow of the Colossus (Best game of Alllll time), Ratchet & Clank series, Jak & Daxter series, Sly series, God of War 1&2 , DMC3, RE4, Kingdom Hearts 1 & 2, Metal Gear Solids, FF XII,  Okami and whatever else I forgot.

Mine would be 
 
-Kingdom Hearts 
-Okami 
-The Jak series 
-Metal Gear Solid 2 
-Digital Devil Saga

socom series 
jak series
ratchet and clank series 
 i'm surprised that no one said socom yet.

Even though I have a lot of favorite games for the ps2 like Shadow of the Colossus and Metal Gear Solid 3. None of them has quite stood the test of time like Devil may cry 3. I still play that game almost everyday.

God of War 1
Soul Calibur 3

Grand Theft Auto: Vice City 
Resident Evil 4 
Persona 3 
Kingdom Hearts 2 
God Of War 1 & 2 
Metal Gear Solid 3: Snake Eater

Never really played much PS2, sadly.  
I'd have to say the three Sly games, Persona 3 and 4, Guitar Hero 1 and 2 and Metal Gear Solid 2 and 3.

games I actually bought this year: 
 
final fantasy 10 .........final fantasy 10-2 ..........ff 12 
Gran turismo 3 
GTA 3 & vice city 
Persona 3 FES & 4

Shadow of the Colossus, Kingdoms Hearts 1 and 2, P3 FES, P4, San Andreas, Resident Evil 4,  and Okami.