Wii U

NES: Super Mario 2
Sega Megadrive: Sonic 3
Handheld Console: Pokemon Crystal
Nintendo 64: Paper Mario
Nintendo Gamecube: Tales of Symphonia
Nintendo Wii: Xenoblade Chronicles
Playstation: Legend of Mana
Playstation 2: Shadow Hearts 2: Covenant
Playstation 3: Dark Souls
Xbox: The Elder Scrolls 3: Morrowind
Xbox 360: Fable 2
PC: The Elder Scrolls 4: Oblivion

Best game of all time: The Elder Scrolls 4: Oblivion
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What in the name of?

Atari 2600: Missile Command
NES: Dragon Warrior 3
Game Boy: Final Fantasy Legend 3
Super NES: Chrono Trigger
Sega Genesis: Phantasy Star IV
Sega CD: Lunar: Silver Star Story
GBA: Final Fantasy V
PSX: Dragon Warrior VII
N64: Mario 64
PS2: Dragon Quest VIII
360: Lost Odyssey
PS3: Skylanders Giants (multiplat, but have it on PS3)
PSP: Legend of Heroes IV: Trails in the Sky
Vita: (going to be) Persona 4: Golden
DS: Nostalgia
3DS: none yet -> (going to be) Etrian Odyssey IV (and later) Dragon Warrior VII remake
PC: Darkspore
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My page on the best site ever for music freaks: http://rateyourmusic.com/~Razor45

NES: a hard call between FF1 and Zelda, think I'd go with FF 1.
SNES: Probably FF3.
PS1: Lunar: Silver Star Story
PS2: Probably Dark Cloud, so many memorable games though.
N64: Can't really say I have too many fond memories of this system, Probably Super mario 64 though real close one between that and Zelda: OoT the only two games that really made this system worth owning.
GC: Metroid Prime
Wii: The Last Story
PS3: Final Fantasy XIII
X360: Think I have to go with Infinite Undiscovery
PSP: Kingdom Hearts: BBS
DS: The World Ends With You

Not even going to do PC, way too many games to think about there. Vita and 3ds are both too new to really put a favorite out yet.

Atari 2600 - Pitfall

Nes - Mega Man II
SNES - Chrono Trigger
Super Famicom - Rockman & Forte
GC - Tales of Symphonia
Wii - No More Heroes
Gameboy - Tetris
Advance - Mega Man Battle Network
DS - TWEWY
3DS - Theatrythym

Master System - Ys
Genesis - Vectorman
Sega 32X - Knuckles Chaotix
Sega CD - Lunar: The Silver Star
Dreamcast - Jet Grind Radio
Game Gear - Mega Man

Playstation - Crono Cross
PS2 - Persona 4
PS3 - Valkyria Chronicles
PSP - P3P
Vita - Ragnarok Odyssey

Xbox - Jet Set Radio Future
360 - Dragon's Dogma

Neo Geo Pocket Color - RockMan Battle & Fighters
WonderSwan Color - Rockman EXE WS
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I'm taking karate classes online

NES-Mega Man 4
GameCube-Star Wars Rouge Squadron II
PS1-Final Fantasy VIII
PS2-Legacy of Kain: Soul Reaver 2
Xbox-Star Wars: Knights of the Old Republic
Xbox 360-Mass Effect 2
Dramcast-Legacy of Kain: Soul Reaver
Nintendo 3DS-Theatrhythm Final Fantasy
Nintendo DS-Dragon Ball Z: Attack of the Saiyans
Gameboy-Legend of Zelda: Links Awakening
Gameboy Advance-Dragon Ball Z: Super Sonic Warriors
N64-Legend of Zelda: Ocarina of Time
PSP-Dissidia Final Fantasy
PC-Vampire the Masquerade: Bloodlines
Nintendo Wii-Super Smash Bros. Brawl

To be fair, there are too many titles to say that this is my absolute favorite of all time. They are ones that I played many times and still enjoy playing.

NES - SMB3
Genesis - Sonic 3 & Knuckles
Game Gear - Dragon Crystal
Saturn - Lets not speak of this
Gameboy - Pokemon GSC
N64 - Perfect Dark
GBA - Golden Sun
Gamecube - SSBM
Xbox - Ninja Gaiden Black
PSP - Cant remember
DS - Cant remember
Xbox 360 - Halo 4
Wii - SMG
PS3 - Uncharted 2
3DS - Sold it after a few weeks of not playing it
Vita - Sold it after a few days of not playing it, realized I'm done with portables

PC pre-2000: Baldurs Gate 2
PC 2000-2005: Morrowind
PC current: Battlefield 3

Only going to list systems that I can instantly list favorites on. I have tons of systems/games and I'm tired.

Intellivision: Burgertime, Diner, Treasure of Tarmin
NES: Crystalis, Mega Man 2, Zelda 2
PS1: Final Fantasy IX, Wild Arms
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Gordon Ramsay, the Mr Resetti of cooking

NES- Metroid
SNES- A Link to the Past
N64- Ocarina of Time
Gameboy- Dragon Warrior III
PSX- The Legend of Dragoon
GBA- Tie between Final Fantasy Tactics Advance and Riviera: The Promised Land.
Gamecube- Luigi's Mansion
PS2- Kingdom Hearts 2
DS- Lunar Knights
Wii- Skyward Sword
PS3- Dragon's Dogma
Xbox 360- Minecraft Xbox Edition
3DS- Virtue's Last Reward
PC- Minecraft
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Not changing this until Capcom either gets their act together or the company goes under (Dragon's Dogma was a good start.)

NES - Megaman 2
SNES - Super Mario RPG
Gameboy/Color - Pokemon Red/Crystal
N64 - Banjo-Tooie
Playstation - Tales of Phantasia
Gamecube - Super Smash Bros. Melee
GBA - Fire Emblem The Sacred Stones
Playstation 2 - I can't really decide, so here's a couple games I really liked: Star Wars Battlefront II, Ar Tonelico, Persona 3 FES...
DS - The World Ends With You
Wii - Super Smash Bros. Brawl
PS3 - tie between Tales of Graces f and Persona 4 Arena
Xbox 360 - Tie between Elder Scrolls V: Skyrim and Tales of Vesperia
3DS - tie between Tales of the Abyss, Kid Icarus Uprising and Devil Survivor Overclocked
PC (90's, early 2000's) - Sonic & Knuckles Collection
PC (modern) Melty Blood Actress Again Current Code

I love me some RPGs and Fighting games.
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"Eirika, Level 20, 7 strength. Should I be concerned?" -Czardia
"It doesn't take that much Str to make a sammich, so she's good." -PokeAMon

Atari Jaguar: Doom (i didn't have many Jaguar games. i hated the system and it's terrible controller, so I picked the game that I hated the least.)

Game Boy: The Legend of Zelda: Link's Awakening (i'm not sure many Game Boy games could compare to this one.)

Game Gear: Sonic the Hedgehog (i didn't own many Game Gear games, but the Sonic game was pretty good.)

NES: The Guardian Legend (rather obscure little treasure from the 80s. This was a vertical shooter mixed with an overworld that sort of reminded me of a futuristic Legend of Zelda with guns/lasers.)

Nintendo 64: Super Mario 64 (tough choice, but I have to go with the first game I got for this system when I was 12, and it blew my mind. At the time in 1996, this was the most amazing video game I had ever seen.)

PC: Ultima Online (one of my favorite games ever.)

Playstation: Final Fantasy VII (i have incredibly fond memories of this game. One of my favorite RPGs ever.)
Honorable mention: Suikoden, Suikoden II

Playstation 2: Grand Theft Auto III (the reason I purchased a PS2.)

Sega CD: Sonic CD (not too many choices here...it's gotta be Sonic.)

Sega Genesis: Wonder Boy in Monster World (lesser-known gem of an action-RPG.)

Sega Saturn: NiGHTS Into Dreams… (one of the few games I owned for Saturn.)

SNES: Chrono Trigger (my favorite RPG ever. I still bust this out from time to time.) Honorable mention: Earthbound, The Legend of Zelda: A Link to the Past

TurboGrafx-16: Bonk's Adventure (tough for me to even remember which games I owned for this system...)

Virtual Boy: Galactic Pinball (it's kind of sad that a pinball game was my favorite game on this eye-straining system.)

Wii: Super Mario Galaxy 2/The Legend of Zelda: Skyward Sword (Incredible games. I couldn't choose between the two.)

Xbox: Halo 2 ( technically never owned an original Xbox, but I did own this game and played it on 360.)

Xbox 360: Skyrim (amazing game with an immersive world.)
Honorable mention: Dark Souls