Do you like Anime, or Japanimation hand-drawn animation associated with Japan? I do.
I think it depends on the story. Like any other genre of media, I'm mostly interested in a good story, regardless of the form it takes.
I is broken down into many different genres and targets a wide range of audiences. You might find something that interests you.
I have heard friends talk about Full Metal Alchemist before. Is that a good one?
That's one I haven't checked out yet. I'll have to see if I can look into that. Anime is distributed theatrically by TV or the Internet. 
It's definitely popular on the Internet. Lots of rabid fandoms out there for different anime series.
There are a lot of different sites (legal) such as Anime Network, Funimation, Crunchyroll (funny name), even Netflix and Hulu