my first one was Saint Seyia, but i was so young that i dont even know what was animes... so i consider my 1st anime (that I watched knowing that it was an anime, in japanese with subs) was Neon Genesis Evangelion ... THAT got me into animes!!!!
I saw Totoro when I was 4 years old but I guess that doesn't count (even though I can remember that time very well). Hmm...It was Silver Fang or Pokémon but at that time I had no idea it was called anime.
My first was Robotech/Macross, but I was pretty young then. Well, unless Transformers counts as anime... that was my favorite show back when I was a kid. Anyway, I didn't really get 'into' it until 6 or 8 years back when I first watched Trigun and Cowboy Bebop and I bought the entire Robotech collection on DVD.
Well, like most people, my first anime was Pokemon/Digimon.
But back then I didn't even know what anime was. xD
When I actually knew what it was, my first was either Outlaw Star or Fruits Basket..I really can't remember now. ^^;
Funny, I never really thought of Transformers as an anime. Speed Racer, yeah, but I just grouped Transformers in with the American cartoons I liked - X-Men, Batman, etc. Maybe because I've only ever seen it in English...
First anime was stuff like DBZ, Sailormoon, Doraemon, Ninja Boys, Mojacko (my fav!), Ranma & etc when 10 years back or so.
But KareKano and Fruits Basket were the ones which got me into this evil world ;3