I don't know which shows were sent in the U.S., but when i was a child, there were many animes in the TV. Inu Yasha, Monster Rancher, Pokemon, Digimon, Sailor Moon and stuff like that. That was my first contact with animes and i liked it so much, that i continued to watch it. I think many people just watch them, because they also watched animes, when they were a child.
@Syphex : Hm, maybe i should watch golden time too. Can you tell me a bit about the story without spoiling too much? Also: Angel Beats > SAO > Elfen Lied > Everything else :P