First Game....

You finished and really felt a sense of accomplishment doing it.  Doesn't have to be the first game you finished just the one that as i said above gave you that feeling of, YES that you remember to this day.  For me it is the original Rygar on the NES.  That one really has stuck with me over the years.  God to think how long ago that was.  Makes me feel old.  At least it's a great memory.

I'm guessing it was either Super Mario 64 or Kirby's DreamLand 2.

Halo was the first game i ever beat.

Mario Party 2. Me and my sister played the shit out of that, and did everything in that game. The accomplishment is that I got to spend time with my sister. She's really not into games.

Putt Putt Goes to the Zoo on the PC if that counts.  If not, probably Spyro the Dragon.

I think mine was Duck Hunt or the original Super Mario Bros.

Super Mario Land probably.  First game I remember having an actual ending that I finished.  I was pretty young and sucked pretty bad at games.  When I finally beat Super Mario Land I nearly cried.

Super Mario Bros. but idk if I really beat it. The earliest game I am 100% sure I beat was StarTropics.

Soldier of Fortune

It was probably Super Smash Bros for N64. Even though it was short I the ending was so epic that I felt like I accomplished something when I conquered the hand!

Starcraft

Super Mario World when I got my SNES for christmas. Although I'm sure I played an NES at someones house before that.

Donkey Kong Country.

the original mario bros on the NES. i was like 5 

Aladdin for the SNES. Wasn't the first game I had, but you can't really beat Ms. Pac-man.

First game I ever finished was Zelda: Link to the Past on the SNES.

Chrono Trigger. I think...it was too long ago..I don't really remember that much from back then..I remember playing a shitload of Chrono Trigger, Street Fighter 2, Battletoads, Mario, Zelda, etc...don't remember what i beat first though.

Super Mario World

I'm not really sure. Probably some PS1 game.

Pokemon red

It was probably Super Mario Land.

The simpsons wrestling

TMNT 2 for Nes

The original Rebel Assault on the hardest difficulty. Was 11 years old at the time.

I don't think I ever finished any games when I was younger, I'm only starting to do so nowadays.

Super Mario Brothers 3 on the NES.

Halo.  Friend and I played through the entire campaign co-op in one night/day.

Neverhood on the PC.

First game to completion: Spyro the Dragon. I was 8 and I'd only played bits and pieces of games up until then, never the full game.

First game with an immense sense of accomplishment: Super Mario 64, got everything possible at the tender age of 9
                                                                                                       Also, I remember thinking the end of Paper Mario was really tough when I was young  and I was immensely
                                                                                                       satisfied after beating it.

Definitely Super Mario Bros. Though that was the first, I felt a much bigger sense of accomplishment after Ninja Gaiden 2 (NES). And even though it felt good, Final Fantasy was a bit of a letdown; by the time I finished I had done so much grinding that the last boss was kinda easy.

Devil May Cry 3. I've never been that challenged in my life. Yes I think its way harder than any Ninja Gaiden game but that's just me.

It was definitely Super Mario Bros. on NES. I used to get so angry at that game, then I got so so good at it. Good times!

the misadventures of Tron Bonne 

Mario Bros. the arcade. I could play forever on 1 quarter.  I usually got bored with it after 30 minutes though & stopped playing.

i think it would have to be super mario bros for the nes, but the game i most proud of is persona 3 that game was insane and epic.

Spiderman on the PC.... although I can't really remember beating it...

GTAIII.

I'd played a lot of games before that, but GTAIII took the amount of enjoyment I could derive from a game to new heights.  Completed it about 12 times now from start to finish.

I think mine was Gunstar Heros on the Genesis.
That was, forever ago.

I can't really remember. My Dad had a load of games on his PC (a 386) so I guess the first game I played would have been Duke Nukem 1.

The first game I bought was Toy Story 2 on the PS1.

Super Mario Land for the OG Gameboy. I really hated the submarine level btw. It was my first "system" and game(besides Tetris of course), and I always had to go over to my cousins if I wanted to play NES. I never got to play anything long enough to beat.

LoZ: Ocarina of Time for the N64. Played and played it and when I completed it I was celebrating. I was quite young so it's something that has stayed with me since. Still love the game and still play it today sometimes.

McKids

That shit was hard

I would have to say, Jurassic Park Rampage for Sega Genesis, then it would have to be, Lttp. 

Super Mario Land for the GameBoy. Nowadays I can breeze through it, but when I was a wee lad, beating the final boss and resquing that princess was a huge accomplishment. Man, I remember how proud I was the first time... and the ending theme was pure awesome.

I don't remember the first game I beat :'(

Pokemon Blue, probably.  Sonic 2, Ristar and Lemmings 1+2 (on the PC) were the first games I can remember playing but I can't remember finishing them.  I wasn't very good at games for a long time, but Pokemon is fairly easy to complete by just sticking with it.