Probably Shinobi on my brother's Commodore 64. I can only remember this game because my other brother was in love with the Ninja Turtles, and I wanted to be just like him so I pretended I was a turtle smashing buttons as a very little kid.
I think the first game I owned as "mine" was a game I got for an early birthday called "Skitchin" for the Mega Drive. Although, this Sega MD was also my brothers that sold everything including my game 🙁 and got a PS1. Funny I periodically remind him he did a dirty thing trading my first game away. We did get an N64 as a joint gift from my Grandad before this I'm sure, GoldenEye days but it doesn't count as it was joint. So was our first PC, with Half-Life and those dial-up connection days but, yeah, after that it all happened very quickly and I'm still loving every minute of the gamer life...
One big thing, looking back, that I really miss? Welcome to Gamespy. Bring back server browsing. I miss it so much.