My first experience with anime was of course, like tons of other people, watching Pokemon and all those kinds of shows on TV when I was little but it never really pushed me further into the medium, after outgrowing those shows I actually picked up a rather negative opinion of anime for a short while, can't really remember why but I just flat out didn't like it.
Ended up making friends with an anime fanatic at high school and during one of our LAN weekends I spotted a show called Afro Samurai on his computer, being a big fan of samurais and swords and Sam Jackson, I thought "what the heck, lets give this a go" and ended up loving it. I remember still not liking the more "Japanese" anime after Afro but was very much looking for more anime to watch that resembles it, finally bit the bullet and gave the dubbed version of Bleach a go, initially disliked it but it really grew on me and next thing I know I was watching the dubs of Naruto, ended up running out of dubbed episodes to watch and moved on to subs, hated it at first but it grew on me as well. Finally moved to Fullmetal Alchemist Brotherhood and that was basically the series that solidified my love for anime, been watching shows ever since.