Here's ones I have seen and liked. Also, the reasons why:
Ninja Scroll: In a fantastic version of 18th century Japan, a wandering swordsman becomes embroiled in a secretive ninja clan and their plans to overthrow the government.
It shows it's age in some places, and also has some icky subtexts in spots. However, it's got a good plot, some good martial arts battles, and some memorably fantastic and grotesque characters. Also, it's feature-length, and thus cheaper than a series.
Gundam 0083: Following a brutal war between the oppressive government of Earth and independence-seeking space colonies, a faction of the colonists hatch a bold plan to steal a wonder weapon, and re-ignite the confict.
The Gundam series is the quintessential mecha drama, and of the many series' under that banner, I liked this one a lot. Yeah, there are giant robots, but it's actually a surprisingly gritty and intense war drama, with the lines between hero and villain becoming blurred, neither side being perfect, and a halfway realistic approach to the tactics of war. Characterisation is okay, and there are some fantastic battle sequences.
Excel Saga: This cannot be described easily. In modern Japan, a secret organisation known as ACROSS seeks to conquer the city and then the world. If they had more than two agents (one of whom perenially dies), they might have a chance.
This series is a rampant paraody of lots of other genres, Japanese or otherwise. The first episode is a bit of an unfunny mess, but it settles down immediately afterwards. Sports dramas, war movies, horror, survival, computer dating games, Power Rangers-esque sentai, post-apocalyptic, androids and mecha all get lampooned in different episodes, and it is quite deranged and hilarious. I'd suggest watching some other anime first, though, or a lot of the gags won't make sense.
Noir: A dark drama series. In modern Paris, a female assassin recieves an unexpected message from a young Japanese girl with a blank memory, and deadly killing skills, who thinks there is something the two of them have in common, the clue being a message in a watch.
It's an interesting mystery and character study, with the attempts to decipher a steadily more tangled conspiracy and the relationships between the two assassins (and two other characters who join later) being key. The build-up is slow, but there's seldom a feeling of treading water, and a very good atmosphere. Worth a look.
Trigun: A post-apocalyptic drama with strong Wild West influences. A peerless gunman with a mysterious past wanders the unforgiving desert of a world that is largely primitive, but with incongruous elements of high-tech. However, as well as being a stone-cold badass, he's also a goofy optimist who gets through a good few of the insanely dangerous situations he ends up in through sheer luck. He also has a code against killing.
It's kind of hard to sum up this series without spoling important plot points. Suffice to say, the world, the backgrounds of the heroes and the way the world turned out all get explained, and it's very interesting to watch. The mood of the series shifts notably--the early episodes are very comedic, but the serious elements quickly catch up and come to dominate. The later episodes especially are a real emotional wringer. Highly recommended.
Read or Die: Yomiko Readman is a meek librarian....with truly extraordinary powers over paper, able to use it to block bullets, create weapons or even in one case, a giant-size paper plane. She works for a secret society of super-powered librarians, who are racing against time to fight a conspiracy that involves cloning evil versions of historical figures and using their super-science devices to uncover a certain very dangerous book.
Again, the summing up doesn't do it justice. There is a weird brilliance about the execution that makes the premise pretty believable--it resembles a very unconventional take on superheroes. High production values, great characters and some brilliant action set-pieces all make this a great choice. Also, the original feature-length version (in three episodes) comes on one disc, so you don't have to commit a lot of money.
