Whoa, old but quality thread. I believe
Mushishi was mentioned previously, but I'd like to second it anyway because it's probably one of the most profound, amazing things I've ever seen condensed into 22~ minute episodes. Easily one of my top 5 favorites of all time.
I loved the heck out of
Mononoke (not to be confused with the Ghibli film) for somewhat similar reasons, although the two are hardly alike outside of the whole "enigmatic, wandering medicine man solves spooky mysteries" setting. Mononoke takes an almost avant-garde approach to animation, with all kinds of crazy texturing (similar to the style of Gankutsuou) and loads of eye candy. Visually striking (if a little jarring at times) and a fantastic horror/mystery atmosphere that so very few anime contain.
Kaiji is another series that totally took me by surprise and blew me away. It's the spiritual sequel to Akagi, a suspenseful manga/anime series about a mahjong prodigy (and totally wicked, even if you know diddly about mahjong, like me). Kaiji shares some similarities, but centers around even more dangerous high-stakes, quite-possibly-life-and-death gambling situations (if you consider walking electrified steel beams between skyscrapers gambling, that is). To call the series "suspenseful" would be a gross understatement. Kaiji himself is as "human" as any anime character I've ever come across, and his mistakes quite often cost him dearly, even as he scrapes by the most hopeless situations. Definitely not the most sunny and bright series I've ever seen, though. Let's just say, I was glad to sit through a K-ON! marathon after finishing Kaiji (no exaggeration). (Spoilers within, but
this MAD is one of the funniest things I've seen in days.)
Plus, any anime with an
OP song by The Blue Hearts is fine by me.
Also,
Detroit Metal City (not-very-SFW link). If you have the slightest interest in heavy metal and don't mind hilarious levels of profanity, you'll probably love DMC. Short episodes, too! (There's a live action film too, but as per usual, it sucks in comparison)
Gag Manga Biyori is another ridiculously funny, short format series.
Also, pretty much anything directed by Masaaki Yuasa (Mind Game, Kemonozume, Kaiba and soon Youjo-han Shinwa Taikei) is guaranteed to be off the charts in weirdness/awesome.
YMMV on any/all of the above, but I consider them to be fairly non-typical by today's moe-polluted standards. A small handful of different, interesting series airing recently, actually - perhaps the future of anime is bright after all!