1. (Classic) Traveller, 1981.
Here we have it, my number one defining game/moment; Traveller.
Growing up my parents weren't gamers, but apparently they had gamer friends. We were at one such gamer friend's house when I was a wee lad of seven and these adults I knew were playing Traveller on a coffee table with dice and lots of sheets of paper with stuff written on them...and a drawing of a spaceship diagram.
They were obviously having a blast. I asked what they were doing and they had me sit in right there on the spot. "Just pretend you're there and tell [this guy] what you want to do." is pretty much all the instruction I got. We were in a space hangar trying to steal a ship or something, I don't remember the details but I was already in love; the concept, the setting, the everything.
They had an extra rulebook that they generously sent home with me with the instructed me to read it and start by making up some characters. I did this zealously and although I never went back and gamed with that particular group, my fate had been sealed. I wonder if all these years later if those guys realize what an impact that they had had on me? This really is it, the single most defining moment that everything else hinges on. Ironically enough, I've never even played Traveller, heh.