From the top of my head:
[li]Texhnolyze [http://tvtropes.org/pmwiki/pmwiki.php/Anime/Texhnolyze?from=Main.Texhnolyze] (Mindfuck set in a dystopian future; themes include: the nature of technology and how humanity treats it)[/li]
[li]Serial Experiments Lain [http://tvtropes.org/pmwiki/pmwiki.php/Anime/SerialExperimentsLain?from=Main.SerialExperimentsLain] (General mindfuck that I haven't dared to completely watch yet. Still from what I've seen...very deep)[/li]
[li]Paranoia Agent [http://tvtropes.org/pmwiki/pmwiki.php/Anime/ParanoiaAgent?from=Main.ParanoiaAgent] (Mindfuck about the dangers of consumerism; very Lynchian, strong focus on "Paranoia" as a theme - hence the name)[/li]
[li]Monster [http://tvtropes.org/pmwiki/pmwiki.php/Manga/Monster?from=Anime.Monster] (Nightmare-Fuel rich crime drama; explores the nature of evil)[/li]
[li]NGE [http://tvtropes.org/pmwiki/pmwiki.php/Anime/NeonGenesisEvangelion?from=Main.NeonGenesisEvangelion] & Rahxephon [http://tvtropes.org/pmwiki/pmwiki.php/Anime/RahXephon?from=Main.RahXephon] (Mindfuck mecha shows laden with symbolism and a strong commentary about growing up among other things)[/li]
[li]Legend Of The Galactic Heroes [http://tvtropes.org/pmwiki/pmwiki.php/Anime/LegendOfGalacticHeroes?from=Main.LegendOfGalacticHeroes] (Space opera. In essence a huge discussion about political systems, the morale of the soldier and the meaning of history)[/li]
[li]Kino's Journey [http://tvtropes.org/pmwiki/pmwiki.php/LightNovel/KinosJourney] (Quiet, episodic, road-movie-like show that is essentially just one large string of different metaphors and the questions they pose)[/li]
Also, Fullmetal Alchemist, Code Geass, Spice & Wolf, Puella Magi Madoka Magica and Cowboy Bebop have some very deep themes going into them, too, but they usually take the back seat to action, character development or plain drama.