Here is an introduction to some great anime, modern and classic, drama, sci-fi, action, and romance. You're guaranteed to find a gem you haven't heard of in here (or you just watch too many cartoons, grow up).
Proof that quality animators haven't left the second dimension behind, including the big guns of Disney and Studio Ghibli and lesser known animators like Sylvain Chomet. Including "Lilo & Stitch", "Spirited Away" and "The Triplets of Belleville"
Critically acclaimed animated hidden gems for adults; or alternatively a great way to speed up the emotional maturation of children. Make sure to check out critically-acclaimed Israeli film 'Waltz With Bashir', based on the graphic-novel.
A big fan of psychological thrillers? Why not check out this collection of anime flicks that combine the intense mental gymnastics of the genre with traditional anime aesthetics. The only thing you have to lose is your grip on reality...