Grr... I hate when I've typed in a long reply then accidentally lose it. I'm going to resort to just listing a bunch of titles. Most of these have complex plots and mature characters. If you'd like a more detailed opinion about any of them, just ask.
Seriei no Moribito
Kemono no Sou-ja Erin (same
author as
Moribito)
Junni Kokuki
Monster
Dennou Coil (If you liked
Noein, you should like this.)
Nodame Cantabile
Welcome to the NHK!
Oh! Edo Rocket (Yes, Sora looks a lot like Eureka.)
Baccano
House of Five Leaves
Bakeneko and its sequel
Mononoke
Claymore
Kurenai
I've largely limited my recommendations to shows released between 2006 and 2009. You'll get more than enough recommendations for recent series like
Puella Magi Madoka Magica from the other denizens at AnimeSuki.