Saw Dragonball/DBZ on TV, Sailor Moon and such.
I think my first experience with anime that piqued my interest was Akira airing on Sci-Fi channel back early 90's.
After Akira, I saw anime around for Fatal Fury, eventually Vampire Hunter D, and I'd pick up a new one here and there to check out when I was bored...
I eventually caught wind of Neon Genesis Evangelion and this is where I got sucked in.
Fuck that was a mindjob for a youngin' like me.
I still have the 13 VHS tapes and most of my DVD's (a missing one or two with a friend.)
After NGE, I was hooked.
Occasional G-Gundam and Gundam Wing on Cartoon Network got me hooked...
I was originally going to name my FFXI character after Kira, Athrun or something from Gundam Seed, but I was San d'Orian and wanted a frenchy name to fit the theme.
I'm a nutjob like the guy anyway, so I suppose the name fits and fits well.
Trigun, Cowboy Bebop, Serial Experiments Lain... Bah, I have to list my small collection sometime on the other thread.
To answer the initial question, I'd say Akira grabbed my interest in anime in general and Neon Genesis Evangelion just slingshot me headfirst into the world of anime and I couldn't stop buying until a year or so ago. >_>;