I saw a bunch of movies with my friends, that was the first time. One loved anime, so we went to blockbuster and rented some. We ended up with this series that was weird, it was about an all boys school, and one of the main boys looked like a girl. All of the guys would look at him in the bathroom and be shocked. The main character had a crush on his sister in law or something, and the class presidents liked eachother... the episode I remember most had some woman who claimed she was sick of "hunting for little boys" and was now moving to little girls. She abducted one to give her pleasure, who was that boy who looked like a girl's younger brother. The woman was disappointed that this girl was actually a boy.
I have no idea what it was called, but we all found it hilarious.
The first I saw that I can remember by name is Princess Mononoke, by the way.
Probably Pokemon, but because I was a wee lass in those times, I wasn't entirely aware that it was an anime to begin with. Yeah, I knew the franchise came from Japan and whatnot, but I didn't know there was a seperate animation term here in the west for their properties. Otherwise, the first one I watched knowing that it was anime was Princess Mononoke. The 12 year-old me couldn't particularly complain about starting off with one of Miyazaki's classics.