I've added "Ghost in the Shell" to my list of current recommendations, but with a few reservations. I think it deserves recommendation for the audio track alone, and the visual look of the piece is absolutely beautiful. The philosophy about what constitutes a human being/person is also great (I particularly love the moment when the protagonist remarks that she thinks that the only thing that makes her human is the fact that people treat her as such), and cleverly interwoven with the story; the political machinations are also believable, and the idea of [spoiler here, but not for the really big twist] using a computer program designed to simulate a terrorist to keep the government in power anticipates both the neoconservative philosophy of solidarity through fear of external threat and the BBC's documentary "The Power of Nightmares" by ten years.
However. The dialogue is flat and boring as all get out (I don't know if it's just a bad translation, or if the Japanese is equally stilted, but either way) and the voice acting is really below par: the protagonist in particular sounds like the director said, when she asked for her motivation, "well, you're a cyborg policewoman with issues about whether you're a robot or a human, so you should say everything in a flat, mechanical voice." Her sidekick manages a bit more emotion, but still sounds like he's ordering out for pizza rather than engaging in high-speed, life-or-death chases most of the time. So my recommendation is: be warned, and ideally watch it in small chunks so that the flatness of the dialogue and delivery doesn't obscure the thought-provoking messages.