It's hard recommending #anime to people whose only exposure has been Dragon Ball Z, Sailor Moon, and Poke'mon - all series meant for a wide or young target audience. It's further complicated because anime is at its best when viewed subtitled instead of dubbed, which many people are reluctant to try.
Here is my list of recommendations, in approximate order, of anime series with great plots or characters that adults should try. These can all be found on Hulu or Netflix, and most are dubbed in English if you just cannot tolerate subtitles (although you lose a lot of meaning that way). You should watch at least the first 2-3 episodes before judging it, as it takes that long to set things up.