In no particular order:

[PS2] (anything not on this list I either didn't play or didn't enjoy)

Ratchet & Clank (series)
Jak & Daxter (series)
Drakan: The Ancients' Gates
Baldur's Gate: Dark Alliance [2]
Champions [of Norrath: Realms of Everquest] / [:Return to Arms]
Metal Arms: Glitch in the System
Shadow of the Colossus
Transformers (2004, NOT the one based on the later movie)
Mercenaries: Playground of Destruction
Darkwatch
Metal Gear Solid [2], [3]
God of War [2]
Metal Slug Anthology ( :D )
Sly Cooper (series)
Shadow of Rome
Spartan: Total Warrior

[PS3]
Ratchet & Clank (series)
Uncharted (series)
Red Dead Redemption
InFamous

...might be able to think of more after I've had some sleep...

[NES]

The Legend of Zelda

[SNES]

The Legend of Zelda A Link to the Past
Super Metroid

[N64]
The Legend of Zelda Ocarina of Time
The Legend of Zelda Majora's Mask
Goldeneye
Perfect Dark
Super Mario 64

[GBC]
The Legend of Zelda Link's Awakening DX

[PS1]
Final Fantasy VII
Final Fantasy VIII
Castlevania Symphony of the Night
Parasite Eve
Parasite Eve II

[PS2]
God of War
God of War II
Final Fantasy X
Ico
Onimusha series
Baldur's Gate Dark Alliance
Baldur's Gate Dark Alliance II

[PSP]
Crisis Core Final Fantasy VII
Silent Hill Origins

[PS3]
Heavy Rain
Uncharted 2
Enslaved Odyssey to the West
God of War III
Killzone 3
Resistance 2

[X360]
Halo 3
Gears of War 2

[WII]
Super Mario Galaxy
The Legend of Zelda Twilight Princess
Metroid Prime Trilogy
Silent Hill Shattered Memories
Super Mario Galaxy 2

Sega Genesis:
-Sonic 1-3
-Shining Force 1-2
-Golden Axe 1-3
-Comix Zone
-Vectorman 1-2
-Dynamite Headdy
-Ristar

SNES:
-Super Metroid
-Super Mario World
-Final Fantasy 4, 5, and 6 (I played the GBA versions but still, although I liked the soundtracks from the SNES better)
-Legend of Zelda: Link to the Past
-Earthbound

N64:
-Legend of Zelda: Ocarina of Time
-Legend of Zelda: Majora's Mask
-Megaman 64 (Well if you don't have a PS1)
-Super Mario 64
-Paper Mario
-Banjo-Kazooie and Tooie
-Pokemon Stadium 1 and 2

PS1:
-Castlevania: Symphony of the Night
-Intelligent Cube
-Megaman X 4-6

PS2:
-Persona 3
-Dark Cloud 1
-Devil May Cry 1
-God of War 1 (Meh...not a fan of the series but good hack and slash to say the least)
-Kingdom Hearts 1
-.Hack//Infection, Mutation, Outbreak, Quarantine
-DBZ Budokai 1
-Jak & Daxter 1-2
-Sly Cooper 1-2

Gamecube:
-Ikaruga
-Legend of Zelda: Wind Waker
-Fire Emblem: Path of Radiance
-Paper Mario: Thousand Year Door
-Sonic Adventure 2: Battle (Heard that there's a PC version coming)
-Luigi's Mansion
-Super Mario Sunshine
-Super Smash Bros. Melee
-Starfox Adventures
-Super Monkey Ball 2

Xbox 360:
-Catherine
-BlazBlue Continuum Shift
-Bayonetta

Wii:
-Xenoblade Chronicles
-The Last Story
-Mario Galaxy 1 and 2
-Legend of Zelda: Skyward Sword
-Sin and Punishment: Star Successor

GB and GBC:
-Legend of Zelda: Links Awakening DX
-Pokemon Blue, Red, Yellow, Gold, Silver, and Crystal

GBA:
-Golden Sun 1 and 2
-F-Zero: Maximum Velocity
-Castlevania: Harmony of Dissonance
-Casltevania: Aria of Sorrow
-Megaman Battle Network 1-3
-Fire Emblem and Scared Stones
-Mario and Luigi: Superstar Saga
-Legend of Zelda: The Minish Cap
-Metroid Fusion and Zero Mission

PSP:
-Final Fantasy 7: Crisis Core
-Kingdom Hearts Birth By Sleep

N64

GoldenEye 007
Perfect Dark

PS1

Parasite Eve
Parasite Eve II
Silent Hill

Updated.

Shadowrun is pretty awesome.

We need more portable console love.

PSP:

Warhammer squad commander

I've already seen so many games listed that I found either completely meh, or even disliked.

Of course all these lists are merely personal... After all, I found PS2 ICO great even quite recently, enjoyed it quite a bit, while I saw some others pan it right after that.

I will rearrange it. And drop some of the games. This is just a draft for now.

good lord forgot these part 2
[Atari 2600]
frogger
missile command
pitfall

[nes]
double dragon series aka controller breakers :D
Adventure Island
bomber man
Darkwing Duck
duck tales
chip n dale

[snes]
Teenage Mutant Ninja Turtles: Turtles in Time
breath of fire series
the 7th saga
secret of mana

[gba]
mother 3
Summon Night: Swordcraft Story 1 & 2

My backlog is large enough already.

I'll acquire console games when they become available on the PC, if ever.

Already have a machine capable of playing games that can do anything consoles can and then some.

In an age where hardware is finally getting consolidated more (TV screens also being computer monitors, internet providing more and more what cable companies used to provide on TV with separate hardware, cell phones backing up as music players and mini-computers), why would you want to waste resources and money on redundant hardware?

Do your part for the environment: give consoles the boot already (ok, consoles that provide unique peripherals like the WII are somewhat better, but still, they really should make those peripherals for the PC and not waste their time re-inventing the wheel).

Call me preachy, but I'm sticking to my guns on this one.

If a game is console only, I'm not interested, no matter how awesome the game is.

There is already a slew of incredibly awesome game on the PC.