Nintendo
NES - Duck Hunt - F*** Yea!
SNES - Donkey Kong Country - Why waste time playing games when it's so nice out (sister made me an addict)
N64 - Mario Kart 64 - Finally an awesome system that's mine!
GCN - Smash Bros - F*** Yea!
Wii - Metroid Prime 3 - This is awesome, but the Hunters make the game feel childish

Nokia
N-Gage - Sonic - This is cool, but I feel like a loser with a gameboy phone

GB - Donkey Kong Land 3 - F*** Yea!
GBC - Pokemon Gold/Silver - MEGA F*** Yea!
GBA - Super Mario Advance - Haha got the system a day before release, this is awesome
DS - Advance Wars: Dual Strike - Hmm.....not as awesome as previous games, but still F*** Yea!
3DS - Fire Emblem Awakening - MEGA SUPER F*** Yea!

Sega
Genesis: Sonic The Hedgehog - Chaos Levels are fun, wait why can't I save? NO!!!!
CD: Sonic CD - Oh man, more of the same? Why can't I see past 10 feet?
Saturn: Panzer Dragoon - Not bad, wish I played this when it was new.
Dreamcast: Sonic Adventure - Dammit Finally, a proper Sonic game! Wicked

Sony
PS1: Driver 2 - Whoah! Awesome
PS2: Gran Turismo 3 - What's FR layout? What do I buy as a first car? This is complicated.
PS3: Resistance - meh
PS4: Yet to see/play

PSP: God of War - Wow I hate GoW, but this is actually kinda awesome

Microsoft
XB1: Crimson Skies - This is fun
360: Gears of War - Holy F***
XB1: Killer Instinct - Meh

Well I don't remember exactly so I will state those that I think it might have been.

NES - Super Mario Bros 3 or The Legend of Zelda
SNES - Super Mario World or Zelda: A Link to the Past
Mega Drive - Sonic 2 or Castle of Illusion
N64 - Super Mario 64 or Zelda: Ocarina of Time
For all above, don't remember which one I played first, but all are great games. Very good impression.

PS1 - Spyro the Dragon
Saturn - Sonic 3D: Flickies' Island
Xbox - Fable
Xbox 360 - Dead Rising
PS3 - Resistance: Fall of Man (pretty ironic since I hate FPS on console)
Wii U - ZombiU
PS4 - Rayman Legends
For the above; okay games, Sonic, Rayman and Fable being the better ones. Mixed impression.

GC - Zelda: Wind Waker
Dreamcast - Shenmue
PS2 - Shadow of the Colossus
Wii - The Legend of Zelda: Twilight Princess
Great games. Enough said. Very good impression.

PC: Rogue, no idea what I was doing, and it was in green/black at the time.


MSX: Athletic land, great fun


PS1: Wipeout, reason I bought the PS1, I've been a fan of the series since
N64: Mario 64, great transistion to 3D although I sucked at it
PS2: Ridge racer 5, it was ok
DC: Crazy taxi, Awesome!!!
GC: Wave race: Blue storm, meh forgot I still had it
XBox: PGR, reason I bought the Xbox, did not disappoint
XBox 360: Call of duty 2, meh
PS3: Resistance, bigger meh
Wii: Zelda TP, good although not as great as windwaker.
WiiU: New Super Mario Brothers U, Awesome platformer we can all play together
PS4: KZ: SF, Awesome sound design, decent campaign.
(XB1: Forza Horizon 2 if bigger size open world this time)

Nintendo
NES - Super Mario Bros.
N64 - Super Smash Bros.
Wii - Super Smash Bros. Brawl
Wii U - Super Mario 3D World

Sony
PS - Crash Team Racing
PS2 - WWE Smackdown! Here Comes the Pain
PS3 - WWE Smackdown vs. Raw 2008
PS4 - Resogun

Microsoft
Xbox - Forza Motorsport
Xbox 360 - WWE Smackdown vs. Raw 2009

Handhelds
Gameboy Advance SP - Pokemon Yellow
Nintendo DS - Pokemon Diamond & Pearl
Nintendo 3DS - Pokemon X/Y
PlayStation Vita - Final Fantasy X

I loved every single one of the games except for Forza simply because I wasn't really into racing games all that much at the time.

Nintendo:
SNES: Ninja Turtles: Turtles In Time- Had me hooked from the very beginning.
N64: Mario 64- Made me a believer in the 3D platformer and the game that convinced me gaming was Art
GCN: Twin Snakes…was the only reason I got a Cube….loved the updated graphics…hated Snake doing his best DMC3 impression
Wii: Twilight Princess…the only game I ever played and beat for my Wii…Nuff Said.

Sony:
PS1: Twisted Metal 2- Meh…didn't really grasp me as much…though I got MGS1 shortly after.
PS2: MGS2- I was floored and captivated…the first game was amazing but (outside of Raiden) MGS2 topped it in so many ways for me…and the way it pushed the PS2 to the extreme…First game to keep me up until Sunrise.
PS3: Resistance- Killer MP mode…great Story and the only good game at launch.
PS4: NBA 2k14…I was so in love with this game. Had my jaw floored when I first boot it up…then came the patch

Microsoft:
Xbox: Jade Empire- I had an Xbox for years and never touched it. Then I got a hold of Jade Empire and was introduced to Bioware.
Xbox 360: Mass Effect- literally everything about this game was amazing. Everything I wanted from Jade Empire and KOTOR on a technical and narrative level were delivered with Mass Effect.

Damn straight.

WiiU: NintendoLand. Fun but uninspired
PS4: Knack. Meh.
XboxOne: CoD Ghosts. Gorgeous but repetitive/boring
3DS: Street Fighter IV. Wow.
PsVita: Mortal Kombat. Wow.

NES: Super Mario Bros. (cool)
Game Boy: Tetris (I still remember the "new" smell of the Game Boy for some reason more than the game. Link play Tetris was a lot of fun)
Super NES: Super Mario World (nice but I wanted to play Final Fight more, I dunno why always liked Mario 3 more than SMW)
Playstation: Jumping Flash! or Battle Arena Toshinden (whoa 3D polygons)
N64: Super Mario 64 (wow)
Game Boy Advance: F-Zero: Maximum Velocity (fun)
Dreamcast: Sonic Adventure (nice, but Soul Calibur blew me away)
PS2: Madden NFL (ho hum)
GameCube: Wave Race: Blue Storm (decent but not mindblowing)
Nintendo DS: Super Mario 64 DS (it's Mario 64)
Sony PSP: Ridge Racer (fairly impressed)
XBox: Dead Or Alive (decent)
XBox 360: Kameo (decent. HD is purdy)
Wii: Wii Sports (baseball is fun)
PS3: Ridge Racer 6 (I think?) or that Motorcross game (lets try the Blu-Ray player)
Nintendo 3DS: Super Street Fighter IV (oooh, the 3D effect works, but not quite how I expected. Still neat).
Wii U: well technically Rayman Legends (demo unit) (fun I guess, controller is big but light)
XBox One: Killer Instinct (E3) (bit underwhelmed)
PS4: Knack (demo unit) (meh)

Of the launch systems I would say SNES, N64, Dreamcast, and PSP made the strongest favorable impressions. 

only going back as far as 7th gen, too lazy.

360 - perfect dark zero : Crap
PS3 - Motorstorm : Crap
Wii - Twilight Princess : Crap
WiiU - Sonic and All-Stars Racing Transformed : Crap
XBO - Froza 5 : Crap, Forza 4 kicks it's ass
PS4 - Killzone Shadowfall : Polished crap