For me, it was during layovers on log bus trips from NC to Ohio and Alabama when my mom and I went to visit family. All the bus stations seemed to have at least a few video games, and the bigger ones (Columbus) had huge arcades that would make it where I didn't wanna leave.
We also used to walk up to a convenience store and play "Phoenix". My uncle, when I visited my grandmother, would walk me up to the 7-11, where he would play Q-Bert all day, and I would read comics (he wouldn't get off the damn machine and let me have a turn....but he bought me Slurpees, so all was good). And on the rare occasions we went to a mall, I dragged my parents into the arcade, which I think the majority of were "Aladdin's Castle".
When I was 4 and living in Columbus, there was a little place called "Bernie's Bagel and Deli" where we would wait for my dad to get off on his half days at work. They had a small place upstairs with Pinballs, and I used to win quarters off of the guys that would go up to smoke and play. I'm pretty sure they were taking pity on a 4 year old that wanted to play, but it was fun! The local Rock station (Q96-FM) let me do the joke of the day one morning, so I have fond memories of that place.
In the 90's it was the bowling alley in Sanford, NC and the mall in Fayetteville, where my best friend and I went to go play SF2, Mortal Kombat, and all the new fighters. I'd still play Pac-Man when waiting for my turn.
As for home systems, I've had a computer since the Vic-20, and I've had almost every game system to date (minus a 360--went Wii and PS3), and still have them all. I still have a "Scramble" tabletop game that I've had since my 7th birthday. I turn 33 this year....it still works fine. I also just got my parent's "Super Pong", which was found in my grandmother's closet. Fun to play on a 53" TV!!
So I guess, I've had games around since before I was born!
Anyways, sirmatt asked, so I thought I'd share!