Loving the suggestions here, especially The Girl Who Leapt Through Time, The Cat Returns and Jin-Roh. Anthony and Ashly, I don't know if you're checking this thread but there's lots of good stuff!
Eternal Family is brilliant. The whole thing is like half an hour long, but it's broken up into 30-second episodes and they're really fast-paced. I love it.
And JoJo's Bizarre Adventure is some damn good fighting anime.
And both of these are on Youtube in their entirety but don't tell anyone