I watched lots of random dubbed animes on Toonami and Adult Swim growing up, but the one that really made me want to watch lots of anime and start watching subbed was Neon Genesis Evangelion. I watched it when I was 10 or so on Adult Swim and it just kinda stuck in my head for a while.
I watched some Dragonball z and Pokemon as a kid but didn't really know what anime was then. I really started to recognize anime while watching Trigun and Cowboy Bebop on Adult Swim. You know, back when AS used to show anime every night. Good times.
Romeo Aoi Sora/Romeo and the Black Brothers/Romeos Simple Dreams: pretty old school anime from my time.
and other World Masterpiece Theater anime, they were all aimed for children and had good lessons and the fact that most of them got aired in the Philippines(that is if you were born in the 90s) so yeah i got into anime coz of these
for everyone here i suggest watching some World Master Peice Theater anime theyre quite good not everyones cup of tea though but still there might be ones that you might like.
heres the list:
http://en.wikipedia.org/wiki/World_Masterpiece_Theater
Sailor Moon and Pokemon. Although, when when I was little, I didn't know Sailor Moon or Pokemon was anime.
Later, when Cardcaptors came on, I figured out that all this is anime.
I started to watch Love hina and Chobits, and so on...
For me it was "Rosario+Vampire"
When i was younger i watched other animes too such as dragonball, zoids, gundams,etc. But i just saw them as just as cartoons but when i got older i saw a difference with art style and so on.