I got started watching anime with DBZ, but that doesn't count in America. It was actually with Boogiepop Phantom on AniMidnight back when TechTV was around. Then I saved up and bought Evangelion, since it's the "all time" need-to-watch... Needless to say it sparked my mind into searching for more, and since then I have delved into it for the past several years.
I've seen shows ranging in genres from Grave of the Fireflies and Kimi Ga Nozomu Eien(which I give high praise for really incorporating their themes) to the quirky, inrealistic and yet beatiful artwork of Dead Leaves. And may Shin Chan like humor please live on.
There is something that anime is capable of doing that live action could never accomplish. The ridiculous reactions, the unbelievable scenery, the drawing(and come on, that's hard to do, let alone come up with), and the idea of voice acting being more perfect for the character than a person manipulating their own in real life...
Needless to say, I do like my anime :)