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If someone's into that stuff, I'd probably start them out on shows like Basilisk and Gantz, maybe a bit of Wolf's Rain and Elfen Lied, too.

Manga-wise, you can't go wrong with Battle Angel Alita, especially once stuff starts to really pick up around vol. 3.

The title of your post is kind of misleading, though. A lot of what people would consider the best examples of seinen or josei might be too slow or cerebral for someone who watches...well, crap. I definitely wouldn't start someone like that out on say, Texhnolyze or something.

I'd say Paradise Kiss (anime), if it's like someone who's in their later teens 17+ or around there depending upon maturity level and all that. Its only 12 episodes, so it pretty much has an episode to set most of the series up and packs a lot of awesome in 12 episodes. So it feels kind of slow, but it leaves you want a bit more. The main character is also a little bit whiny and hesitant Similarly to most shoujo manga, but not nearly to that extent, nor is it that irritating.

Hrm...maybe I should list them here. ;)

Berserk--the violence shown in here is never senseless and silly. It always gives that feeling of tragedy and so forth.

Tsukihime--very interesting supernatural visual novel series with the right level of darkness to be seinen, but I also like the manga version of it, since it closely follows the visual novel. :)

Fate/Stay Night--also a wonderful seinen visual novel. Action-packed as well.

Ghost In The Shell: Stand Alone Complex--very action-packed robotics/cyberpunk seinen anime.