I know what you are looking for since I personally like these kinds of stories best myself. You might want to look into....
[ul][li]Monster [http://tvtropes.org/pmwiki/pmwiki.php/Manga/Monster?from=Anime.MONSTER]: Psychological thriller that deals with the nature of evil - has some of the most haunting scenes I've ever seen, without ever resorting to overtly crazy stuff. Perhaps the most "western" anime you will ever see.[/li][/ul]
[ul][li]Legend Of The Galactic Heroes [http://tvtropes.org/pmwiki/pmwiki.php/Anime/LegendOfGalacticHeroes?from=Main.LegendOfGalacticHeroes]: The quintessential space opera and a show that is essentially about that the world, history and politics is essentially grey. Very cerebral and in a classical sense one of the most "epic" shows I could ever see.[/li][/ul]
[ul][li]Samurai X - Trust and Betrayal [http://tvtropes.org/pmwiki/pmwiki.php/Manga/RurouniKenshin?from=Main.RurouniKenshin]: anime movie that is a heartwrenching tragedy. Maybe a bit presumptions at times still utterly beautiful in a very depressing way[/li][/ul]
[ul][li]Spice & Wolf [http://tvtropes.org/pmwiki/pmwiki.php/LightNovel/SpiceAndWolf?from=Main.SpiceAndWolf],Higurashi - When They Cry [http://tvtropes.org/pmwiki/pmwiki.php/VisualNovel/HigurashiWhenTheyCry?from=Main.HigurashiNoNakuKoroNi] and Puella Magi Madoka [http://tvtropes.org/pmwiki/pmwiki.php/Anime/PuellaMagimadokaMagica]: All of those might be too tropy for you but the second is disturbing horror (and sometimes too over the top) and the third one of the best tragedies I've seen so far. The first is what I like to call the prime example of a character driven anime-show that is essentially just about a developing romance - sounds boring but is a very sincere show and far more tragic than one thinks if one looks a little bit beyond the surface. Highly recommended [/li][/ul]
...or if you want something more cerebral and/or disturbing (e.g. think David Lynch or some thoughtful movie but as an anime)
[ul][li]Kaiba [http://tvtropes.org/pmwiki/pmwiki.php/Anime/Kaiba]: Disturbing Cyberpunk that deals with the issue of identity and broadly with body-soul problem. Very bleak and enigmatic despite its style. [/li][/ul]
[ul][li] Paranoia Agent [http://tvtropes.org/pmwiki/pmwiki.php/Anime/ParanoiaAgent]: Broadly a critique of consumerism this one is the perfect example of what would happen if David Lynch directed an Anime. Starts pretty normal, becomes a depiction of paranoia and then goes into cloud-cuckooland.[/li][/ul]
[ul][li] Kino's Travels [http://tvtropes.org/pmwiki/pmwiki.php/LightNovel/KinosJourney]: Very quiet show that essentially asks the viewer what to make of the things portrayed. Something that gets you to think well after each episode. [/li][/ul]
...or something more pop-corny (think 24 but as an anime)
[ul][li] Death Note [http://tvtropes.org/pmwiki/pmwiki.php/Manga/DeathNote?from=Main.DeathNote]: A rollercoaster anime classic which is sometimes well over the top but never too much to become annoying. It just stays awesome[/li][/ul]
[ul][li] Cowboy Bebop [http://tvtropes.org/pmwiki/pmwiki.php/Anime/CowboyBebop?from=Main.CowboyBebop]: Another classic and a show that I can only describe by asking "What if Quentin Tarantino did anime?". Not an exact comparison thanks to his latter movies but still - the atmosphere it certainly has.[/li][/ul]
ninja666 said:
The Japanese are a pretty immature bunch and it shows in all of their creations (schematic, full of same archetypes, over the top badassery and peculiar type of humor that isn't funny unless you are "brainwashed" enough)
Well tbh that can also be said about most Western sitcoms if you swap Japanese with US-american and minus the badassery...for that we have Chuck Norris...