First I ever saw was Kiki's Delivery service from a Blockbuster. I had to have been about 3, so I'm surprised I remember it as well as I do.
Then pretty much only Pokemon and DBZ for a long time.
Wasn't until I lived somewhere that actually had Cartoon Network that I got into it.
I credit Trigun with actually getting me into Anime.
Somewhat related to what Ax was saying, did anybody ever get really into the Abridging scene ?
What ones got you into it ?
Which, if any, do you watch now ?
Yu-Gi-Oh Abrigded, the great granddaddy of the whole thing was the first for me. I was huge into ARDBZ.
My favorites were Lani's Yu-Yu Hakusho and Malakodistudios Hellsing.
(Malakodis' episodes are disappearing)

I only watch TFS's DBZ these days.