Commodore 64 - can't remember the name of the game, was basically racing blocks on the screen (in 3D though!).

Super Mario World.

I was 2 years old and only finished it when i was 6 xD

Pong.

On a Philips Tv Game ("Telejogo" in my country), like this one, in 1982:

Duck Hunt

The monochrome resolution made me a better gamer.

The first game I owned myself was Pokemon Sapphire, but the first game I've ever played was probably Donkey Kong Country (yes I almost cried at the DKCR announcement ^^)

Duck Hunt

Haha I remember these things!

The Legend of Zelda: Ocarina of Time, and I have been a huge fan of the series since then. 

Combat on the Atari 2600.  I have no idea why my father bought the system out of the blue, it just wasn't something you'd expect from him at all.  Not in a million years.  I guess it was mostly for my older sisters but it wasn't long before I took the Atari over completely and was begging them to play against me.  Thankfully, that was when games started to appear in the bargin bin for $5, so I was able to move on to single-player stuff.