Although I think your definition of "mature" is a bit juvenile, here's some excellent anime that fit your criteria:
Elfen Lied is exactly what you want (save for the nudity bit).
Akira is also what you'd like and a must watch for anyone who wants to call themselves an anime fan.
Neon Genesis Evangelion is another good, mature anime. It starts off as a typical shonen mech show, but turns into something very, very different later in the series.
Puella Magi Madoka Magicka is, despite first appearances, also up your alley. Give it until the end of episode 3 before making any judgements.
Higurashi no naku koro ni (and its second season, kai) is pretty gruesome throughout much of it. It's well regarded by most fans, although I personally didn't like it as much.
And although there's no gore (save for maybe one scene), Grave of the Fireflies is both dark and tragic, as well as probably being the most artsy film on this list.
With the exception of Higuarshi and Elfen Lied, I would consider everything on that list to be mature (my definition of "mature" being a show that has a plot that takes itself seriously and doesn't resort to edginess for the sake of edginess).
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