When I was real young, I used to play Neo Geo games and not even realize it: Puzzle Bobble, Magical Drop II, 3 Count Bout, World Heroes, Art of Fighting, Cyber Lip, Thrash Rally... all these machines at pizza places and malls and stuff.
The very first Neo Game I ever remember playing and thought "this is special" was Samurai Shodown II.
After that, I did some research and found out all my favorite games happen to be Neo Geo titles... Then, when I started playing KOF 98, I knew I'd one day own a machine.
Thankfully, I later found out about how to build a CMVS and things got a lot easier