But you have Perfect Blue, which is really serious.
Perfect Blue is more like a movie that happens to be animated. Like that WW2 one, can't remember the name. Exceptions, not the rule, etc. More often than not I find that anime can't pull off compelling stories to my liking.
As the resident animu maniac, I can tolerate serious stories in my animu, but it's definitely the case that some shows just get too
serious business and end of flopping, when they could have kept being light and fun. It's also the case that a lot of anime simply don't have a very good story, so ramping up the story and getting serious turns the whole thing into a boring mess.
However, I can probably come up with a few that would still interest you:
The Big O - Noir mecha series, it's basically a bunch of the guys who animated Batman: TAS getting together and deciding to do the Japanese version of it. Some parts of the main story arc are kind of ridiculous [especially when everything comes to a head at the end of the second season], but a lot of the one-episode stories are really, really good. It's the kind of show that I can watch over and over because the stories, characters, and the world are just so compelling.
Patlabor the Movie 1 and 2 - These two are like Tom Clancy stories in animate form. There's intrigue, government corruption, rumination on the nature of war and peace, and giant robots [which Tom Clancy stories desperately need, in my opinion]. They have action scenes but they're not action movies, they're political dramas.
Witch Hunter Robin - it's basically The X-Files with witches and the people who hunt them. Most of the show is episodic, but the second half drops in the story. Not the best I've seen, but it's got a great gothic atmosphere and the main story isn't too bad.
Ghost Hunt - an animated version of all those ghost show documentaries, except the ghosts are real. It's actually a series of arcs without any real central arc, just a setup. Surprisingly good, this was one that I just picked up on a whim because it looked interesting. It's got a lot of genuinely creepy and scary moments.
Time Stranger - now here's a really obscure anime movie. It's actually the sequel to a giant robot fighting force series that probably no one can remember, but rather than simply being a movie version of the series, it's actually a psychological drama that has more in common with Watchman than Volton. It really surprised me by how good it was. It's a dark show with dark themes, but feels justified in going that route. Don't worry about the series, the movie offers enough setup that it's pretty easy to tell what's going on and who everyone is.
Ghost in the Shell: Stand Alone Complex - easily one of the best written animes of this decade, series or movie. It's got great characters, great stories, great music, and great settings. It's the best of the best and always brought up in recommendation threads for a reason. It's a must if you like speculative scifi.
Kino's Journey - basically a series of philosophical quandaries as witnessed by a stoic, gun-toting girl and her sentient motorcycle. Not every episode is serious, but most of them are. It's one of my favorite shows, but I can see how a lot of people would really be turned off by it. Most of the time is moves slowly and is more concerned with examining some aspect of human thought or action, but never quite coming up with an answer. Good for when you want something to think about, not good for when you just want to chill out and see dudes beating on each other.
