Having to recently field this question a chunk; yeah, check out Cowboy Bebop. Good dub, as was Trigun. If you want something that plays a little more like a good sci-fi drama on US TV, Witch Hunter Robin. Me personally, I enjoy my fantasy with some steam-punkish mecha, and healthy dose of dramatics- Escaflowne (the series, don't bother with the movie), was very good for this. These are all 26 ep 'light snacks' as most anime fanatics call them. I don't have the time for the long hauls, and as such, have only bothered with a slight few...and I don't think Reboot counts, sadly... anyway, Samurai Champloo's got a great art style, good soundtrack, and memorable characters- and the writings not too bad, either. Could also recommend the original 13 episode OVA set of Tenchi Muyo, along those lines. After that set, it gets...'weird'... it's worth it, but build up your tolerance of anime weirdness first (FLCL).
Of course, if you'd like the non-traditional, slow approach, rent some Miyazaki films first. 'Howl's Moving Castle', was well handled in translation. 'Spirited Away' was also, surprisingly, enjoyable. 'Vampire Hunter D', or 'Perfect Blue'. Oh, and 'Tokyo Godfathers'. That covers a very broad range of movie types from horror to humor, comedy to creepy. There's sites out there, I assume, or you could just check the netflix directory for ratings and types. right, night!