Yeah, if you’re looking for strong, capable female characters, stay far away from Death Note.
My recommendations:
Monster, a psychological thriller. It’s got fantastic writing, a complex storyline, and lots of great character development. In a very rough nutshell, it’s about a surgeon who’s chasing after a serial killer. That doesn’t nearly do it justice, but it would take too long to explain the entire synopsis. Very dark story, and very creepy, with one of the most terrifying villains I’ve seen in fiction, let alone anime. It’s about 74 episodes long, so it’s a bit of a commitment, but not a single one is wasted.
One Piece. A cute, funny, and awesome action shounen about pirates. This one’s even longer–more than 400 episodes, and with no sign of slowing down–but it’s actually one of the rare shounen that gets BETTER the more episodes it has. Though it’s a kid’s show, it has a great story, very smart writing, and kickass scenes. It runs the gamut of emotions: there have been scenes where I’ve laughed my ass off, scenes where I’ve cried buckets, and scenes that made me want to stand up and cheer. It’s zany and wacky and fun and amazing. One caveat, though: DO NOT WATCH THE 4KIDS ENGLISH DUB. It’s getting harder to find anyway, so you may not even encounter it, but if you do watch an English dub, make sure it’s the one done by Funimation. People think the fans exaggerate when they talk about how horrendous the 4Kids dub is, but they really, really don’t. It really is that bad.
Paranoia Agent. Continuing with the Satoshi Kon theme–it’s a very surreal show about a mysterious attacker called “Li’l Slugger.” It’s definitely weird and creepy at times, and since it’s supposed to be a commentary on Japanese society, there are times when I was fairly sure there were cultural references I was missing, but it’s very good nonetheless.
Sayonara Zetsubou Sensei. A comedy about a high school teacher in Japan and his various students. Quite funny, but also very pretty, with better-than-average animation and art. This, IME, is actually fairly unusual for a comedy–I’ve found that comedies tend to skimp a bit in the animation department, while the dramas are usually prettier. Again, it’s a commentary on Japan, so again, the culture differences might be a bit confusing, but still great stuff.
Baccano! A sci-fi-ish series that takes place in the late 20’s-early 30’s and features a group of people who are immortal. Cool, stylish story with great characters and awesome action.
All right, that’s enough for now.