The very first experience, if it can be called one, was back in 1995 at the school. Some kind of formula racing on a PC (probably). Though I was allowed just to press some buttons, crash and that's it - other, older kids took over, crowded the place and I lost interest pretty soon.
Later, 1996, my uncle had a NES hardware clone going by the name of Zhiliton. Most likely the famous Duck Hunt was the very first game, most likely because of the gun. I mean - you can shoot at the telly and things happen - how awesome is that!
And, of course, I later beat my uncle's records by standing close to the telly and just shooting the wretched things as soon as they appeared
There were some other, too - some kind of Kung Fu I totally sucked at, Tetris, Lode Runner and a truly lame casino he used to play himself the most for some reason. No Super Mario, Mega Man or any other "classics" till much later when some more involved friends from school lent me some games - new cartridges were really expensive, I don't remember buying any on my own.