It was 1982.  I was either 6 or 7 at the time.  I have a brother and sister that are several years older than me, and they pooled their money together and bought an Atari 2600.  They initially had two games: Combat and Adventure.  Adventure is still an awesome game that I like to play to this day.  It was like the godfather of the Zelda series.  Not long after, my siblings bought a bunch of other games: Space Invaders, Asteroids, Missle Command, and several others.  These games were so much fun to play and they were nice enough to let me have plenty of turns.  Then Pac-Man came out and this game sucked on the Atari 2600.  It seemed like my siblings lost interest shortly after getting this game, but I still loved video games, so I basically inherited the system from them, and I kept getting video games for Christmas and stuff.  All the kids on my block had an Atari too.  It was awesome!  It was 1982.  It was the best time ever for a kid to discover gaming!

The next year was 1983.  I kept getting Atari games.  I'd get some money for good grades; buy a game.  Grandparents would visit; get a game.  Birthday?  More games.  As the year progressed I kept getting fun arcade ports: Donkey Kong, Kangaroo, Elevator Action, ....  For some reason, the games kept getting cheaper and cheaper at the stores.  And while all the kids played Atari at the beginning of the year, by the end of the year almost no one else was playing Atari.  No one but me.  And I was running out of new games to play.  New games just weren't coming out anymore, but I didn't realize it until the end of the year.  Then it seemed like all the games were gone, nobody cared, and there was no indication that the games were ever coming back.  It was terrible!  It was 1983.  It was the worst time ever for a kid to discover gaming!

Flilix said: I'm too young for the poll. The first games I played were PC games for kids, I think the very first one was called Klikkerdeklik. The first 'real' games I got were Pokémon Emerald and Disney's The Wild, which I both got together with a Game Boy Micro when I was 6 years old.

"I'm too young for the pole." #nameofyoursextape.

:)

December 15, 1988. My second day in America after moving from Jamaica at age 7. My neighbor from across the street comes over with his NES. I’d never seen a video game system before and it was quite interesting. The very first video game I played was Double Dribble. We went from that to Contra, then Life Force, then Rygar, and a few other games I can’t really remember. Been a gamer ever since. Those were the days...

Didn't know we were going to get philosophical here, but your point is well taken.  We all do this...a lot.  Dreams become memories, our family's stories about us become memories, and our false recollections do as well.  It certainly makes finding the facts in our history difficult.

For me it was probably Donkey Kong Jr on the Atari 2600.  Great graphics, great gameplay.  Just an overall great experience for the time.  It's possible the actual first game may have been Combat, since I loved that game and played it a bunch, but Donkey Kong Jr was the experience I was most enthralled with at the time.  This is probably around 1982.

that would be this beauty :

I still have mine, bought in 83' right before the crash. Was 8 when I got it. 43 games, 3 regular, and 2 Super Action controllers. 2600 was my first, but this blew it out of the water. I had the trackball and steering wheel, but returned them because they didn't work properly. Basically useless/unsupported peripherals. 

Pitfall on Atari 2600. It is actually one of my earliest memories. I was 2 (I think) at the time.

First video game I played must have been one of those LCD games. Got my first one during a visit to Melilla.

https://www.youtube.com/watch?v=2MDoBcCZUQQ

If we are talking home consoles, then I also remember playing the NES at a friends house. Can't remember if it was Mario first, but I do remember messing with the Zapper and Duck Hunt.

NES at home. But before that Atari at a friend's place.

Super Mario Bros. Duck hunt combo for the NES. Magical times. Second I remember was Zelda II it was such a dark and mysterious game. I was five then but still even though I couldn't get far into it Zelda always had a special allure for me.