Most of these didn't exactly "change my life", per se, but they
did change my way of thinking:
Cowboy Bebop- the first really mature anime I ever watched. It's what got me hooked in the first place. (I also have this show to thank for inspiring me to name my Welsh Corgi "Ein".) The characters, music, action, quotes, and overall uniqueness are hard to top.
Trigun- I didn't know that sci-fi and westerns could mix until I watched this show.
Plus, Vash is just such a compelling character.
FLCL- Crazy, lightning-fast-paced, and with more puns than you can shake a baseball bat at. Even with all the aliens, guitars, robots and disfunction, the story is still somehow identifiable. I had to watch the whole series a couple times through before I could even understand it, but once I did, I realized just how awesome it was.
Spirited Away- How can I explain my love for this show? Well, after the first time I saw it, I watched it every following day for the next two weeks. No, I'm not exaggerating. I was that obsessed.
Princess Mononoke- Hayao Miyazaki is a genius. That's all I can say.
Since I've already named so many, I'll leave the rest for a later post.
Sorry about the length.