Here's my favorites:

NES: (I dint own one, but have some VC versions)
1. Mega Man 2
2. Super Mario Bros. 3 (I own the 16 bit version)
3. Startropics (really underrated!)

SNES:
1. Super Mario RPG
2. Donkey Kong Country 2
3. Super Metroid

N64:
1. Zelda Ocarina of Time
2. Jet Force Gemini (My first 3rd/1st person shooter!)
3. Banjo Tooie (Super Mario 64 would be my 4th)

NGC:
1. Zelda Wind Waker
2. Metroid Prime
3. Pikmin 2

Wii:
1. Zelda Twilight Princess
2. Super Smash Bros. Brawl
3. Super Mario Galaxy

NES
1. Super Mario Bros.
2. Megaman 2
3. Super Mario Bros. 3

SNES
Don't have any

N64
1. Super Mario 64
2. Mario Kart 64
3. Super Smash Bros.

NGC
Don't have any

Wii
1. Super Mario Galaxy
2. Mario Kart Wii
3. Legend of Zelda: Twilight Princess

EDIT: forgot about handhelds
GBA:
1. Sonic Advance
2. Pokemon Sapphire
3. ...didn't have any others

DS Lite/ DSi
1. Sonic Rush
2. Final Fantasy Crystal Chronicles: Echoes of Time
3. New Super Mario Bros.

NES: 1) Link's Adventure 2) Legend of Zelda 3) Marble Madness
SNES: 1) Earthbound 2) Super Mario Kart 3) Tetris Attack
N64: 1) Goldeneye 2) Smash Brothers 3) Extreme G
GCN: 1) Smash Brothers 2) Four Swords Adventure 3) Ikaruga
Wii: 1) Smash Brothers 2) Bit Trip Beat 3) Swords and Soldiers

GB/GBC: 1) Metroid II 2) Mario Land 2: Golden Coins 3) Link's Awakening
GBA: 1) Mother 3 2) Mario Kart Super Circuit 3) Tactics Ogre
DS: 1) Contact 2) Metroid Prime Hunters 3) Yoshi's Touch N Go

Virtual Boy: 1) Wario Land 2) Mario Clash 3) Jack Brothers

Yes! More than one person didn't list SM64 in their Top 3 favourites.
Also, Adam, shouldn't WiiWare be separate or not included at all?

NES: 1) Punch-Out!! 2) MegaMan 3 3) Kirby's Adventure
SNES: 1) Donkey Kong Country 2) MegaMan X 3) Super SF2 The New Challengers
N64: 1) StarFox 64 2) The Legend of Zelda Majora's Mask 3) Space Station: Silicon Valley
GCN: 1) The Legend of Zelda Wind Waker 2) Super Smash Bros. Melee 3) F-Zero GX
Wii:1) Super Mario Galaxy 2) Super Smash Bros. Brawl 3) The Legend of Zelda Twilight Princess

GB/GBC: 1) Pokémon Silver 2) Kirby Tilt 'n' Tumble 3) Super Mario Bros DX
GBA: 1) Mario Kart Super Circuit 2) Pokémon LeafGreen 3) Sonic Battle
DS: 1) Kirby Canvas Curse 2) The World Ends With You 3) Pheonix Wright Ace Attorney Trials and Tribulations

NES: 1) Zelda 2) Punch-Out 3) Duck Tales
SNES: 1) Smash TV 2) Mario Kart 3) Pilot Wings
N64: 1) Ogre Battle 2) Ocarina Of Time 3) Pilot Wings
GCN: 1) Midway Arcade Treasures (SmashTV arcade FTW) 2) Zelda GC 3) Mario Sunshine
Wii: 1) Endless Ocean 2) Baroque 3) Punch-Out

GBA: 1) Golden Sun 2) Golden Sun 2
DS: 1)Broken sword 2) Nanostray 3) Mystery Dungeon

I have no GB titles in mind.

Here's my favorites:

NES:
1. Super Mario Bros. 3
2. Legend of Zelda
3. Simon's Quest

SNES:
1. Chrono Trigger
2. Terranigma
3. Super Mario World

N64:
1. Banjo Kazooie
2. Super Mario 64
3. Zelda: Ocarina of Time

NGC:
1. Ikaruga
2. Luigi's Mansion
3. Pikmin 2

Wii:
1. Super Mario Galaxy
2. Klonoa
3. Kororinpa

GB:
1. Super Mario Land. 2: 6 Golden Coins
2. Dragon Warrior Monsters
3. Adventure Island 2: Aliens in Paradise

GBC:
1. Dragon Warrior III
2. Kirby Tilt 'n Tumble
3. Shantae

GBA:
1. Densetsu no Stafi 3
2. Golden Sun
3. Wario Land 4

VB:
1. Wario Land
2. Mario Tennis
3. Vertical Force

NES
-Punch-Out!! Featuring Mr. Dream
-Super Mario Bros.
-The Legend of Zelda

SNES
-Super Mario World
-Legend of Zelda: A Link to the Past
-Super Metroid

N64
-Legend of Zelda: Ocarina of Time
-Goldeneye: 007
-Banjo-Tooie (Such an under-rated game)

Gamecube
-Legend of Zelda: Wind Waker
-Super Mario Sunshine
-Agressive Inline (whoa! How's that for a curveball?)

Wii
-Metroid Prime 3: Corruption
-Super Mario Galaxy
-Punch-Out!!

It's funny, of all the consoles, the Wii was the hardest to pick. It actually might be Nintendo's best console.

Whoa! Forgot about handhelds. I never owned a GB or GBC, so here we gooo

GBA
-Wario Land 4
-Legend of Zelda: The Minish Cap
-Metroid Prime: Fusion

NDS
-Legend of Zelda: Phantom Hourglass
-GTA: Chinatown Wars
-Mario Kart DS

NES:
The Legend of Zelda
Super Mario Bros. 3
Castlevania 3

SNES:
Super Metroid
Super Mario World
Super Castlevania 4

N64:
Mortal Kombat Trilogy
Beetle Adventure Racing
Paper Mario

Gamecube:
Resident Evil 4
Sonic Mega Collection
Mario Kart Double Dash

Wii:
Mario Kart Wii
House of the Dead Overkill
Toki Tori

NES:
Super Mario Bros
Super Mario Bros. 3

SNES:
Super Mario World
Donkey Kong Country
Madden '96/Super Mario Kart/Mortal Kombat II

N64:
Pokemon Stadium
Mortal Kombat Trilogy
Super Smash Bros.

Gamecube:
Super Smash Bros. Melee
Fire Emblem Path of Radiance
Mario Kart Double Dash

Wii:
Super Smash Bros. Brawl
Fire Emblem Radiant Dawn
Pokemon Battle Revolution

DS:
Pokemon Platinum
New Super Mario Bros.
Ultimate Mortal Kombat

SNES > DS > GC > Wii > N64 > NES in terms of original games imo

NES
1. The Uninvited: A "point & click" game for the NES. I liked this game so much. Rented it, but could never find it to buy anywhere. It will be a MUST download when/if it ever hits the VC.
2. Deja Vu: I have this game for my NES right now. Its another "point & click" game for the NES. Fun game.
3. Super Mario Bros. 3: I still remember when I saw the movie, The Wizard, and this game was revealed. I couldn't wait to play it. Still a classic game!

SNES
1. Chrono Trigger: A very classic RPG. Great story, cool graphics, fun gameplay, and multiple endings. Really wish this would appear on the VC. I would buy it in a heart beat!
2. Final Fantasy 6: Possibly the best Final Fantasy game ever! A great game in any case. Classic!
3. Earthbound: Believe the hype. Earthbound is: wacky, crazy, fun, suprising, funny, and just one of my favorite SNES rpgs. In fact, this is the first RPG that I actually liked! Before Earthbound, I didn't like rpgs. Earthbound is just a classic and I wish they'd just put in on the VC already. I also wish they'd just do a sequel for the Wii or DS! sigh

N64
1. Legend of Zelda: Orcania of Time: One of the best Zelda games. I never got to play this all the way through till I played the VC verison. I never owned a 64. Just like this game a lot.
2. Super Mario 64: Really fun. I finally bought this for the VC awhile back and its just a classic Mario game.
3. Mario Kart 64: Great two-player, love the battle mode.

Gamecube
1. Animal Crossing: This is the game that started my Animal Crossing addiction. A friend told me about this, I read about it some, had some extra cash, and took a chance on it. Possibly the best decision I've ever made!
2. Legend of Zelda: The Wind Waker: Great Zelda game. Love the cel-shaded graphics. Glad they have continued that on the DS.
3. Metroid Prime: This is the game that first sold me on the Gamecube. I was so blown away by the graphics on this game and loved the gameplay. I have to get the new Metroid Prime Trilogy Wii collection when it comes out. That'll be great.

Wii (so far)
1. Animal Crossing: City Folk: The best Animal Crossing game so far. Very addictive and the online play is the best Nintendo has so far imo. Can't stop playing this game.
2. Legend of Zelda: Twilight Princess: IMO, the best Zelda game yet. Great graphics, fantastic gameplay, lots to do and explore. Hope the next Zelda game is even better!
3. Super Maro Galaxy: Wow. What a game. Can't wait to play Mario Galaxy 2.

DS (so far)
1. Animal Crossing: Wild World: Another Addictive Animal Crossing experiance.
2. Legend of Zelda: Phantom Hourglass: I am still amazed by the graphics on this game. It looks a lot like the Gamecube Wind Waker game and plays just as well. Fun.
3. Final Fantasy 4: Very good remake of a classic game.

DF2506

NES:
1) Ninja Gaiden
2) Little Samnson
3) Super Mario Bros 2(USA)

SNES:
1) Donkey Kong Country Trilogy
2) Chrono Trigger
3) Yoshi's Island / Super Mario RPG

N64:
1) Super Mario 64
2) Banjo-Kazooie
3) Star Fox 64

GC:
1) Mario Kart DD
2) SSmash Bros. Melee / Soul Calibur II
3) Super Mario Sunshine / Star Fox Adventures

Wii (so far):
1) Mario Strikers Charged
2) Super Paper Mario
3) Super Mario Galaxy

GB:
1) Mole Mania
2) Bubble Bobble
3) Pokemon Red/Blue

GBC:
1) Pokemon Pinball
2) Zelda: Oracle of Seasons
3) Hamtaro Ham-Hams Unite

GBA:
1) Super Mario Advance Series
2) Drill Dozer
3) Golden Sun series

DS:
1) Kirby's Canvas Course
2) M vs DK 2: March of the Minis.
3) Super Princess Peach / Zelda: Phantom Hourglass

NES:
1) Legend of Zelda
2) Super Mario Bros. 3
3) Contra

SNES:
1) Super Castlevania
2) LoZ: Link to the Past
3) Final Fantasy 3 (or FF6)

Wii:
1) Mario Strikers Charged
2) Rock Band 2
3) Mario Kart

GB:
1) Lock N' Chase
2) Tetris
3) Kid Icarus

DS:
1) Castlevania: Dawn of Sorrow
2) Elite Beat Agents
3) Dragon Quest IV

WiiWare:
1) Bomberman Blast
2) Defend Your Castle
3) FF4:AY
I haven't played enough games from the other systems to make a good list. Also, is anybody keeping track of favorites? Would be cool to have a graph of common favorites or something.

NES
1: Bubble Bobble
2: River City Ransom
3: The Legend of Zelda

SNES
1: LoZ A Link to the Past
2: Zombies Ate My Neighbors
3: Super Mario World

N64
1: 007 Goldeneye
2: San Francisco Rush
3: Turok 2

GCN
1: LoZ Wind Waker
2: Need for Speed Most Wanted
3: Resident Evil 4

Wii
1: MadWorld
2: SSB Brawl
3: Sonic and the Black Knight (Suck on that)

WiiWare
1: Bubble Bobble Plus!
2: Bomberman Blast
3: Defend Your Castle
(these are all the wiiware games I own)

GBA
1: SMA3 Yoshi's Island
2: Pokemon Emerald
3: Pokemon Fire Red
(only gba titles I've played)

DS
1: Sonic Rush Adventure
2: New Super Mario Bros.
3: LoZ Phantom Hourglass

Omg list threads !!!1

GB(C)
1) Legend of Zelda : Links Awakening
2) Pokemon Gold / Silver Edition
3) Tetris

NES
1) Super Mario Bros. 3
2) Kirby´s Adventure
3) Mega Man 3

SNES
1) Super Metroid
2) Street Fighter 2
3) Super Mario World

N64
1) Super Mario 64
2) Mario Kart 64
3) Legend of Zelda : MM

GBA
1) Metroid Fusion
2) Golden Sun
3) Doom

Cube
1) Metroid Prime
2) F-Zero GX
3) I have no idea...

DS
1) GTA: Chinatown Wars
2) Henry Hatsworth
3) Tetris DS
note: I could easily make a Top10 with true favorites here, man what a nice system...

Wii
1) Super Smash Bros Brawl
2) Metroid Prime 3
3) Super Mario Galaxy

NES
Super Mario Bros
Super Mario Bros 2
Kid Icarus

SNES
Super Metroid
Super Mario World
Star Fox

N64
Super Mario 64
LoZ: Majora's Mask
Paper Mario

GCN
Metroid Prime
Resident Evil (remake)
Fire Emblem: Path of Radiance

Wii
Fire Emblem: Radiant Dawn
Resident Evil 4
Super Mario Galaxy

GBA
Fire Emblem
Advance Wars
Chu Chu Rocket

DS
Advance Wars: Days of Ruin
Rhythm Heaven
Kirby: Canvas Curse

I see no reason for that at all. I'd take those two games over most disc releases so far. Also, Brawl is the only game on disc I feel is worth owning at the moment (and I gave Wii Sports to my brother who somehow lost his ).

But if I for some reason had to separate them, it would be:
WiiWare: 1) Bit Trip Beat 2) Swords and Soldiers 3) Mega Man 9
Wii: 1) Brawl 2) New Super Mario Bros. 3) Wii Sports Resort

Yes, I can see the future.

NES: 1:The Legend of Zelda. 2: Punch Out!! 3: Super Mario Bros. 3
SNES: 1: Loz: A Link to the Past. 2: Kirby Super Star. 3: Super Mario World.
N64: 1: Zelda: Ocarina of Time 2: Zelda: Majora's Mask 3: Pokemon Stadium 2.
GCN: 1: Super Smash Bros. Melee 2: Pokemon: XD Gale of Darkness. 3: Zelda: Wind Waker
Wii: 1: Super Mario Galaxy 2: Mario Kart Wii 3: Super Smash Bros: Brawl.
GBA: 1: Pokemon Firered 2: Yoshi Topsy Turvy 3: Kirby: Knightmare in Dreamland
GBC: 1: Pokemon Crystal 2: Tetris 3: Powerpuff Girls (Lol)
DS: 1: Pokemon Platinum 2: Kirby Super Star Ultra 3: New Super Mario Bros.

NES
1.) SMB3 2.) Final Fantasy 3.) Faxanadu
SNES
1.) Final Fantasy 3 2.) SM Kart 3.)
N64
1.) SM64 2.) LOZ:Oot 3.) Quest64
GC
1.) Skies of Arcadia Legends 2.) Harvest Moon: A Wonderful Life 3.) Animal Crossing
Wii
1.) AC: City Folk 2.) GH 3.) HOTD:Overkill
WiiWare
1.) FFCC:My life as a king 2.) World of Goo 3.) Dr Mario Online RX
GB
1.) FF Legend 2 2.) Super Mario Land 2 3.) Crystalis (GBC)
GBA
1.) FF Tactics Advance 2.) Golden Sun 1 3.) Tactics Ogre
DS
1.) SM64DS 2.) FF4 3.) Lego Batman (This one is too hard to call really)
DSiWare
1.)Dr Mario Express 2.) Artstyle: AQUITE 3.) N/A
Sega Master System
1.) Double Dragon 2.) Phantasy Star 3.) Section Z
Sega Genesis
1.) Phantasy Star 4 2.) Castlevania Bloodlines 3.) Altered Beast
Saturn
1.) Dragonforce 2.) Shining: The Holy Ark 3.) Nights into Dreams
Dreamcast
1.) Grandia 2 2.) Skies of Arcadia 3.) Shenmue
Sega Game Gear
N/A (I did not play it enough to have a favorite)
PS1
1.) FF7 2.) FF Tactics 3.) Legend of the Dragoon
PS2
1.) Midnight Club 3: Dub 2.) FF 12 3.) RE4
PS3
1.) Elder Scrolls 4 2.) MotorStorm 3.) Rockband
PSP
1.) Midnight Club 3: Dub 2.) SOCOM 3.) NFS:Pro Street
Xbox
1.) Elder Scrolls 3 2.) Fable 3.) Knights of the Old Republic 2
Xbox 360
1.) Elder Scrolls 3 2.) Fable 2 3.) Midnight Club 4: LA

I thought I'd build on Adam's idea...Enjoy!