I have Fullmetal Alchemist (my fav!) Escaflowne, Perfect Blue, Akira, Appleseed, and Rahxephon. I have a few Initial D DVDs, and it looks promising. Wolf's Rain also looks promising.
The ones I've found extremely boring are Cowboy Bebop, Inuyasha, and Sailor Moon. The first two I have no clue of why anyone would like it, and Sailor Moon looks like it would appeal to either men or lesbians.
Hmm, I'll have to find the Excel Saga series. Sounds like the humor in "Family Guy" or "American Dad" on American TV.
My tastes may be a bit more lighthearted than what you're looking for, but my recommendations are here. And a few additions, mostly series that are running now.
-Paranoia Agent. Definite must-see
-Hidamari Sketch. It may not be "mature" enough for you, but I loved it.
-Darker than Black
-Gakuen Utopia Manabi Straight
-Hayate no Gotoku
-Touka Gettan. Confusing but awesome. Gorgeous art and character design
-School Rumble and SR: NIgakki
-Seto no Hanayome. Mermaid yakuzas. Hilarity ensues
It is such an awesome anime. I think it was originally a live-action series, though. If you've ever seen Golden Boy, it's a lot like that... this dude basically touches people's lives through very, well, unconventional teaching methods.
It's the perfect mix of comedy, action and drama. I think it's one of the few anime that, if re-done for a live-action English adaptation, would be very successful among all demographics here in the States. It's a great show.
I also recommend: FLCL, Cowboy Bebop, Azumanga Daioh, Trigun and Big O (which is eerily similar to Batman).
I love Great Teacher Onizuka, because it's funny and it's real. I mean, sometimes one could get tired of all the magic and odd fantasies created in anime but GTO is real and mature but funny, very funny. I also recommend the live action.
GTO is about a guy whose goal suddenly is to be the greatest teacher in the world. In fact he is a horny and former gang leader or something like that who knows karate. At first he is only taking the job to sleep with high school girls, but then he notice all the problems the students have and helps them. コールだよね
i also like GTO! almost finished all 42 episodes and also watched two episodes of the live action (i.e. the version with real actors), which is quite good, to my surprise! besides it gives a nice impression of japanese school life (the uniforms, ways of addressing teachers/students etc.).
Devil May Cry
D. Gray Man
Fate/ Stay Night
Engage Planet キスダム
Full Metal Panic!
Neon Genesis Evangelion
Any of the GUNDAM
まぁ～これは十分だぜぇ～ Don't think that I am an オタク! I'm NOT