I would definitely check out Ghost in the Shell.
There's two versions, the original, and the re-animated version which uses the same soundtrack. The re-animated version is called Ghost in the Shell 2.0, not to be confused with Ghost in the Shell 2: Innocence, which is the sequel. Either version of the original is brilliant, but I prefer the re-animated version.
It's a great cyberpunk Cyborg detective tale, with heavy visual influences from Blade Runner.