High School of the Dead: I must say I laughed at that one! There was this one scene where one of the girls was startled and she turned around suddenly and her boobs jiggled crazily! It was the funniest thing ever! So ridiculous but also entertaining!
How could I forget Ghost in the Shell: Innocence. Along with Cowboy Bebop it was my introduction to anime. Fabulously beautiful renderings.
I'm curious how AngelBeats changed the way you look at the world, since, to me, it seems to be just short of outright kiddie porn.
Anime has been such a large part of my life for so long, it's very difficult to choose. But the series I thought of when I saw this thread is Last Exile. I'm talking about the original, although Fam has it's merits. I watched it with my brothers on TechTV, the channel that would later merge with G4, about 10 years ago. I could go on and on about it.