I need to kill some time before the Fall TV season gets into full swing, so let's try this.
Favourite genre(s): mecha, sci-fi, psychological, action
Previously-liked anime, manga, or movies: Akira (yes, I'm that old), Gundam 0083, Infinite Ryvius, Vandread, Death Note, Valvrave the Liberator, Kill la Kill, SAO, AoT
Specifics you're looking for: Short, concise story, requires a bit of thinking, preferably newer (within the last five years)
Desired length: Nothing long-running, maybe 26 episodes tops. Episode length doesn't matter
Anime you've already seen: (older) Anything ever shown on Toonami, Escaflowne, Gurren Lagann, RahXephon, Neon Genesis, Avatar, Hunter x Hunter, anything Gundam (newer) Tokyo Ghoul, C, Tiger and Bunny, Psycho-Pass, Accel World, Legend of Korra
Anything else? One of my coworkers suggested Magica Madoka, but I haven't gotten around to it yet. If the series starts off with a strong story-arc and tries to shoe-horn another arc into the last couple of episodes (Gurren Lagann, SAO, AoT, Tiger and Bunny, etc.), just give me a heads up.