Hm.  A lot of my "first games" were pretty underwhelming.

Atari 2600 - Combat.  My father brought the system home as a surprise.  He had no idea it needed other games or he probably would not have bought it.  If you've never played it, it's SUPER basic, makes Space Invader seem advanced.  It was really funny to see the tank battle in Saint's Row IV.

NES - Mario.  I wasn't impressed with either it or Duck Hunt.  Luckily, the local video store had many other games for rent.

SNES - NBA Jam.  A fun game to play with a friend but it got boring fast.  I usually picked Larry Johnson.

PSX - Final Fantasy 7.  It was the reason I bought the system in the first place.

PS2 - I really have no idea.  I played so many games on that system that it's all blurred.  Edit:  I think I've remembered!  I THINK it was a game titled Okage: Shadow King.  I loved the style but I remember almost nothing else about it.

PS3 - Valkyria Chronicles.  Amazing that my first PS3 experience was one of the best games of the generation.

Vita - Wipeout 2048.  Damned hard.

Dreamcast - Maken X.  Crazy game.  I want a remake.

Atari 2600: Pole Position (second was ET) Spent hours playing that game at a cousin's house, and never could get out of a pit in ET.
Colecovision: Burger Time, I scarcely remember it
Turbographix 16: Bonk, I'd like to see this game get rebooted
3DO: Dragon's Lair, played it at some tech convention when I was a kid, fuck that game

NES: Super Mario Bros, I still suck balls at this game
SNES: Super Mario World, my all time favorite Mario game
N64: Mario 64, always thought it was overrated
Gamecube: Wind Waker, didn't like the cell shaded graphics at first, but it really grew on me
Wii: Wii Sports, meh
Wii U: New Super Mario Bros U. MEH
Gameboy: Link's Awakening, My all time favorite Zelda, dat windfish
Virtual Boy: Wario Land, pretty good game, just on a shit system
GBA: Metroid Fusion, played it on the toilet
3DS: Link Between Worlds, disappointing

Genesis: Sonic, decent
Saturn: Panzer Dragoon, pretty good
Dreamcast: Grandia 2, damn good game
Game Gear: Sonic whatever, even color couldn't defeat gameboys three shades of doom

Playstation: Symphonies of the Night, tits, just, fucking tits man
PS2: I think it was whatever the first Madden was to come out for it, can't remember
PS3: Valkyria Chronicles, WOW
Vita: Sly Cooper 4, just played a demo at a store, don't own one, only way I'll get one is if it comes bundled with a ps4 in the near future

Xbox: Jet Set Radio Future, awesome game, great soundtrack
Xb360: Orange Box

PC: Battle Chess

SNES- Super Mario World. was such a hard game but something made me come back for more

N64- I think Mario Kart 64 was one of my first N64 games, just so much fun

Wii- Wii Sports, need I say more?

Wii U- The Legend of Zelda: Windwaker HD. Introduced me to one of my now favourite franchises

PS1- Micro Machines V3. great multiplayer game, even by yourself lol

PS2- GTA Vice City. Amazing game, amazing music. Still go back to it every now and then

PS3- Uncharted 2: Among Thieves. I was mindblown by the graphics and it was a very interesting game. Made me realise how good naughty dog are.

Saturn- Sega Rally. one of my favourite racers ever..

Dreamcast- Metropolis Street Racer. Up there with sega rally, shame bizarre are no longer with us :( PGR and Blur were great too!

Handhelds
Game boy- Tetris. Instant classic

3DS- Donkey Kong Country Returns 3D. very fun but very hard

PSP- The Simpsons Game. Just like the show, I love it

Vita- Uncharted: Golden Abyss. Great game

I'll go in chronological order:

Coleco Vision: Donkey Kong, wow, I fell in love with video games in my cousin's basement! (I must have been 5 or 6 at the time).

NES: Metroid, this game was amazing for the time, what no levels, you can go wherever you want (I did not figure out how and what to do until much later)

Sega Master System: Phantasy Star, 3D dungeons, battles with backgrounds that change according to where you are, etc. again a game that blew my mind!

Turbo-Grafx 16: Keuth Courage in Alpha Zone, I liked the graphics, but it kind of let me down.. the action was good, but repetitive in the robots part... I liked the machine when I got R-Type, Blazing Lasers... but never got over buyer remorse for it and eventually got a Genesis like most of my friends back then.

Sega Genesis: Golden Axe, loved this game, especially with some friends to finish it in two player mode! hack and slash galore... too bad a good sequel was never released.

TurboDuo CD: Ys Book I & II wow CD games are the future!

Sega CD: Sherlock Holmes, FMV based games suck...

Super NES: F-Zero, loved the smooth mode 7 race track, the music... it's still one of my favorite racing games!

3DO: Need for Speed, I was amazed by the texture mapped 3D graphics, the sounds, it felt "real"

Sega Saturn: Panzer Dragoon, I liked it, the story line, etc. but wondered why the videos were not full screen.

Play Station: Final Fantasy VII, I was blown away, played through in 56 hours in less than a week!.. then did another play through with a manual and leveled up all my characters to level 99 + found every single objects with my room mate of the time!

N64: Zelda Ocarina of Time, liked it, but stopped at the water dungeon (I had a gaming PC at that time, so n64 graphics/frame rate were a real indrance to my enjoyment of this game).

Sega Dreamcast: Soul Calibur, it was amazing looking and extremely fluid, made me love the machine from day one.

OG xbox: unsure, everything seemed generic to me on this machine, but it was clearly the most powerful console of its day, but I was mainly gaming on PC.

GameCube: Mario Sunshine, I liked the clean graphics and the water effects, but over all this machine never got much appreciation since I played mainly on PC during that time too.

Wii: Zelda Twilight Princess, I had waited so long for this game.. but really found that the controller held it back and stopped playing at the escort mission... sold the Wii before it lost value.

xb360: King Kong, the game's frame rate seemed choppy to me, it did not make a good impression and I never got a 360 (even if I eventually tried gears of war).. again PC got in the way of awe...

PS3: Wipeout HD.. it left a pretty good impression, I did not really play much games on the PS3 until GoD of war 3, Uncharted 2... etc. got it for media functions first.

Ouya: Final Fantasi VI... this console is weak...

PS4: Killzone:SF this console is amazing!

xb1: Forza 5, why do people think this machine can hold its own against the Ps4?

Wii U: Rayman Legends, this could be on PS360 easily.

ATARI 2600 - ... don't remember first game. pretty sure I received a collection of games at first. may have been asteroids or 1942 or similar, etc.

NES - SMB, awesome game... loved it. (received duck hunt, hogan's alley, and ice climber along with it)

SNES - Super Metroid, best in series ever. (got SMW a little later, bought this SNES 2nd hand)

N64 - SM64, amazing game... got it with Wave Race

NGC - Metroid Prime, like M64 it was a great update to a great series.

Wii - ZeldaTP, loved it!... got it with wii sports, wii play, excite truck

PS3 - Assassin's Creed, very good story and ok gameplay

WiiU - ZombiU, so scary and emotionally charged... got it with NintendoLand, CODBLOPS2, and NSMBU a couple days after

This game--may not have been the first I played but good lord, when I played it...wow.  After over 100 hours of Soul Blade on the PS1, I knew the next gen had arrived big time.  And when I played the demo disc that had Dead or Alive 2, I was even more impressed!

SNES - Starfox (Holy crap this is epic!)

Megadrive - Sonic the Hedgehog (Why do you go so fast you can't even see what's coming?)

PS1 - Croc: Legend of the Gobbos (Wow, it looks and sounds so beautiful!)

Saturn - Panzer Dragoon (Fantasy Starfox, cool!)

N64 - Lylat Wars (It looks so real!)

Dreamcast - Shenmue (Who the hell dubbed this, a bunch of stoned teenagers?)

PS2 - [Can't remember]

Gamecube - Rogue Squadron II (This is like movie graphics!)

Xbox - Jedi Starfighter (Why doesn't it look as good as Rogue Squadron if Xbox is more powerful?)

360 - Halo 3 (Hmmm, not that different from Halo 2...)

Wii - Wii Sports (Now THIS is next gen!)

PS3 - COD MW2 (Did Michael Bay direct this game?)

Wii U - COD BO2 (Finally, the franchise does something new! Also, pointer controls + modern graphics = awesomesauce)

Xbone - Forza 5 (Not a bad way to kill some time at EB games waiting for a date)

PS4 - Killzone Shadowfall (I can't remember another shooter where I spend less time actually shooting things)

NES: Super Mario Bros with Duck Hunt - Fun, but hard as hell (I was 3-4 by then). I only remember having the Duck Hunt pistol.

SNES: Super Mario World - I remember being glued to the seat for hours, going thru the worlds. I loved the mystery feeling the game gave: looking for the switch palaces to unlock the missing blocks, discovering secret passages and castles, defeating annoying bosses, make Yoshi eat the secret key (which was the most hilarious thing ever), discovering the Special world... Mario's highest point. One of my favorite games ever.

PS1: Gran Turismo - An awesome and addicting game. I always used to play Arcade with my cousin and always chose the Nissan Skyline R34 GTR with a manual transmission. I always lost, but I always had a blast.

N64: Super Mario 64 - Beautiful game with whimsical music and solid gameplay. I still remember sliding down the slope, trying to beat the penguin and cutting corners to win.

PS2: Grand Theft Auto 3 - The most mind blown I've ever been. I remember playing Driver 2 a lot back then, so looking that superior 3D world and the Yakuza Stinger drifting across Liberty City made me realize that the game was a revolution. A step forward for gaming.

PS3: Grand Theft Auto IV - A damn good, solid game. Loved roaming around the dark metropolis while listening Oxygene Pt. 4 or Waters of Nazareth. Good story made me want to experiment every story choice available. Loved it.

Pc - Doom - very addictive and scary as hell at the time.
Sega something -sonic something - boring as hell. Hated 2d games and I still do.
Nintendo 64 - perfect dark - impressive but didnt compare with pc shooters.Terrible controller.
Ps1 - tomb raider and resident evil - fun but fustrating controls put me off.
Dreamcast - soul calibur - great, best fighting game I played at the time.
Ps2 - gta3 - boring, couldnt get into it but anticipated the pc release. Other y1 games failed to impress. Poor controller.
Xbox - Halo and Splinter Cell -First console games to truely blow me away. Got me into consoles. Started the trend of seeing better looking games on consoles than on Pc's.
Xbox 360 - GRAW - Great game, amazing graphics. Best controlef I have ever held.
Ps3 - killzone 2 - bored me to death. Rubbish controlls.
Xbox One -Titanfall - most fun shooter in years, but not really a next gen game
PS4 - Killzone 4 - bored me even more than kz2.

*paws at Duck Hunt*