Most of the shows that I'd suggest have already been mentioned, but let me toss out a couple more:
Monster
At root a meditation on the psychology of evil, Monster is one of the most compelling shows I've watched in any medium.
Ghost Hound
A strange brew of brain science, psychology, philosophy, and mysticism presented in a beautifully animated package with an extraordinary sound track. GH is definitely one of the more underappreciated shows of 2007-08.
Ergo Proxy
Like Evangelion, Ergo Proxy wants to discuss philosophical issues in a science-fiction package, and like NGE its reach often exceeds its grasp.
Black Lagoon
Beneath the gunfire lies an existential plot. The last story arc (ep 19-24) specifically discusses Sartre and Heidegger. The Wikipedia article has an interesting discussion of the philosophical issues raised in this show.