I'm a nasty little Grinch.
Is topic anime only, or also manga allowed?
Will try to follow all topic's title, topic's actual mood and Extreme's comment above.
Listing most... "prominent" anime/manga I've stumbled with, and marking with '*' those I'd say "liked the most".
Anime:
Fullmetal Alchemist Brotherhood*
Ergo Proxy*
Serial Experiments Lain*
Tsukihime
Kara no Kyoukai
Fate/ sagas in general
Monster* (interesting indeed, but *extremly* slow)
Mushishi*
The Twelve Kingdoms
Perfect Blue
Tasogare Otome x Amnesia* (manga as well)
Another*
Tokyo Godfathers
Sci Fi Harry*
Mirai Nikki*
Jormungand*
Paprika*
Paranoia Agent*
Summer Wars*
Toki o Kakeru Shoujo
Wolf Children
Night at the Galactic Railroad* (what a great bittersweet piece)
Brave Story*
Mononoke Princess
Howl's Moving Castle
Spirited Away -Sen to Chihiro no Kamikakushi-*
Kiki's Delivery Service*
Death Note
Accel World* (+note at bottom)
Sword Art Online
Akira*
Cowboy Bebop
+Too bad it got a shameful OVA instead of a due next season; worse, OVA took *right were LNs are* and author is seemingly no longer taking his works that seriously... correct me if wrong please.
Manga:
Narutaru
Bokurano*
Deadman Wonderland
Oyasumi Punpun* (perhaps the best I've ever liked until now)
Uzumaki
20th Century Boys* (same author as Monster)
Ane Freaks*
Aku no Hana
Rozen Maiden (anime part as well; disappointing indeed...)
I omitted some others due to believeng they're already of strong public domain.
Quite an interresting list, you might wanna look into Boku dake ga Inai Machi ("Erased") and Break Blade (or Broken Blade), they could fit in there quite well.
I didn't watch Monster yet, only read the Manga; but if you liked the author you could try Pluto (also by Naoki Urasawa). Currently reading the books of Juuni Kokuki, and I'm not gonna finish them any time soon for the sheer amount of them :x