In some vague sense of order:

Half Life 2

Deus Ex

System Shock 2

ICO

Silent Hill 2

Grim Fandango

Shadow of the Colossus

Elite

Uncharted 2

Ultima Underworld 2

Honourable mentions for being small but perfect: Portal & Flower

Honourable mentions for being games I loved the concept of, but not totally the execution : Oblivion, Fallout 3 and the STALKER games.

In that order.

1. FFX
2. Persona 3 FES
3. MGS 3
4. FF VI
5. Digital Devil Saga 2

Ooof, that's a toughie.

I have some great games to finish playing (Baten Kaitos Origins, Tales of Symphonia, New Super Mario Bros Wii, Metroid Prime Trilogy, Final Fantasy's) so I have to get back to you.

I can give a definite #1 though. Kingdom Hearts 2.

1.Zelda:Ocarina of Time
2.Zelda:Majora's Mask
3.Mario Galaxy
4.Super Smash Bros Brawl(hands down my best multiplayer.yes,I have never played a game online before & yes,I have played MW2's spec ops)
5.Metal Gear Solid 3:Snake Eater
6.All the Metroid games I've played(for some reason,I like em all equally)
7.Golden Sun 2(GBA)
8.Zelda:Twilight Princess(I haven't played WW & I have all 2d zeldas but haven't played over an hour in any yet!)
9.DragonballZ games generally

1. Shenmue (Sega Dreamcast)
2. Streets of Rage 2 (Sega Megadrive)/Guardian Heroes (Sega Saturn) i simply can not choose one over the other
3. Fighters Megamix (Sega Saturn)
4. Sonic and Knuckles (Sega Megadrive)
5. Resident Evil 2 (Sega Dreamcast)

Have to also mention my fave racer....... Need For Speed: Hot Pursuit 2 (XBOX)

1. Warcraft 3 (PC)
2. Ragnarok Online (PC)
3. Need for Speed: Carbon (PC)
4. Kingdom Hearts 2 (PS2)
5. Final Fantasy XII (PS2)
6. Rappelz (PC)
7. Knights of the Old Republic II (PC)
8. Knights of the Old Republic (PC)
9. NeverwinterNights 2 (PC)
10. 9Dragons (PC)
11. The Elder Scrolls IV: Oblivion (PC)
12. Valkyrie Profile: Lenneth (PSP)
13. Virtual Tennis World Tour (PSP)
14. Virtua Tennis 3 (PSP)
15. Tekken: Dark Resurrection (PSP)
16. Ridge Racer 2 (PSP)
17. Final Fantasy VII (PS1/PSN)
18. Prince of Persia: Revelations (PSP)

Don't know why i chose 18, got lazy. xD

1. Metroid Prime. GC, Nintendo/Retro Studios, 2002
2. Sonic Adventure 2. DC (though i played it on GC), Sega/Sonic Team, 2001
3. Super Smash Bros Melee. GC, Nintendo/HAL Laboratories, 2001
4. Phantasy Star Online Episode I and II. GC, Sega/Sonic Team, 2002
5. Super Mario Galaxy. Wii, Nintendo, 2007

1 - Shenmue
2 - Phantasy Star IV
3 - Mass Effect
4 - Elder Scrolls IV
5 - Zelda: Ocarina of Time

Also

Full Thruttle
The Dig
Mario RPG
Kotor

So many games, so many memorys..