I believe my first anime, way before I knew what anime was or what Japan was, for that matter, was the Ultraman anime. Formulaic as hell, but I enjoyed it thoroughly every day after kindergarten... Formulaic, that is, until the main character died and went to some Ultraman heaven o.o That changed my life a bit.
Afterwards... Dragonball, Dragonball Z, Rurouni Kenshin, Digimon, Pokemon, Sailor Moon, Detective Conan, The Kickers... basically the whole RTL2 lineup, even though I hardly understood any German.

First one I watched intentionally, stuff on TV aside, would have to be Street Fighter 2: The Animated Movie. That changed my life, man. Watch it, if you have the opportunity and enjoy yourself some good, fun martial arts action.
Also (and this is the only time I've said this about any anime), avoid the original dub. The music is far, FAR superior in the English dub, trust me. Unless you're into techno/J-pop during your hardcore fight scenes.