Ah yes, let me tell you ALL ABOUT my obsession with One Piece. I have seen the first 300-something episodes of One Piece three times over, is how much I love it. I'm a few episodes behind right now - I'm on episode 690, I think - and I don't keep up with the manga because of reasons, but yes.
One Piece. It is.... oh my god, it is the best thing. I know it's aimed more at teenaged Japanese boys, and not so much at 27 year old Swedish women, but good GOD is it ever right up my alley. I just have a gigantic soft spot for underdogs rebelling against the world order, desperate last stands, passionate people fighting other passionate people, impossible odds, optimism bordering on the suicidal and plenty of dorky jokes. I just love the way One Piece centers around a sort of fierce humanity, which is SO not what you'd expect out of a series that is basically The Adventures Of The Ridiculous Rubber Pirate.
Let's just say I appreciate a story that can do serious critiques of oppressive governmental systems, expose the evils of slavery AND pull a few jokes about how the main character stuck chopsticks in his nose and thinks it's hilarious - in the span of a single episode.
Other favourites (and note that this list is seriously influenced by a.) what was/is available in Sweden, b.) that I am kind of seriously out of the loop on more current anime)):
Trigun
FLCL
Samurai Champloo (which may mor may not have had a teeny-tiny influence on Grassblades)
Windy Tales (this one is a bit more obscure, but well worth watching! Quirky animation, low-key slice of life. Cats.)
Lots and lots of Ghibli movies
The first Fullmetal Alchemist-anime (as in, not Brotherhood. I know the first anime adaption departs heavily from the manga, but considered on its own, it is actually a really good story. But let's not mention Conqueror of Shamballa, which ruins the entire ending of the first anime).