It's been mentioned once, but I'm going to put in a vote for Ghost in the Shell: Stand Alone Complex. For anyone who likes CSI, Law and Order, NCIS, etc. it's the perfect intro to anime. It focuses on a Cyberpunk Task Force that specializes in cybercrimes. It combines action, investigation, political intrigue and can get a bit cerebral. I would recommend introducing someone to the series first, then the third movie, Ghost In the Shell: Stand Alone Complex: Solid State Society, which continues the storyline from the series, before going back to the first two movies which have their own separate continuity.
Another good intro anime is Trigun. It starts out as more of a Western before gradually bringing in more complex influences.