(I got a bit tired, and didn't describe what's found in some of them, if interested, you can ask me and I'll answer/tell/explain what they have in them)
Violence: specifically psychology/behavior+theory of war and fighting (extremely intelligent/sophisticated/high level knowledge):
Mobile Suit Gundam Wing, an anime series of ~50 (if my memory is working, lol)episodes
high level romantic uber witty-teasing romantic relationship:
Spice and Wolf (1 and 2), an anime series
philosophical mind-soul (soul = your "Ghost")-psychology:
Ghost in the Shell: Stand Alone Complex (1 and 2 as GitS:SAC 2nd Gig), an animes series
lots of very good psychological characters and themes:
Claymore, the manga especially, but also the anime series too. Priscilla is the most psycho character you'll ever encounter, Roxanne is really creepily wicked, Ophelia is quite messed up too, and Rubel SCARES me, the sociopath of sociopaths, when Rubel says to hop and ribbit like a frog, god hops and ribbits like a frog! ...

(Claymore is my FAV !!!! hehe)
Memories:
Big O, an anime series
some interesting perspectives on life and quite some psycho characters:
Black Lagoon (1 and 2) and
Black Lagoon: Roberta's Blood Trail ("3"), 2 anime series and 1 OVA-anime "series" (4-5 episodes long only, lol)
some good psychology:
Blood+, an anime series
Fullmetal Alchemist and
Fullmetal Alchemist: Brotherhood, two different-versioned anime series (Brotherhood follows the manga)
Phantom: Requiem of the Phantom, an anime series
Soul Eater, an anime series
Solty Rei, an anime series. Girls, if you want to understand a man truly (his often hidden emotions, psychology, feelings, and thoughts): Roy Revant.
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and for non-manga/anime:
The Dark Knight movie: The Joker, hehe
.