*shrug* Like everything else, there's good ones and bad ones. And enough different ones to appeal to all sorts of different types. (The ESFP-shounen hero going on a enthusiastic journey to become the best ___ has the most esposure to the general public, I think, and possibly is what turns off a lot of people in this thread?)
Anime-cons, on the other hand, only appeal to about four types: 1) crazy fan-girls; 2) crazy fan-boys; 3) Comic Book Guys (who come in sole hope of complaining in great detail with fellow comic-book-guy's while in line for something.

These showdowns to determine who can reference more obscurely are quite entertaining, so they serve a purpose.); 4. attention whores
A few good ones off the top of my head:
Great Teacher Onizuka- an ENFP gangster tries to become a great teacher through his unorthodox methods and despite his students trying to sabotage him at every turn
Escaflowne- A very INFX fantasy-adventure about a girl who gets involved in a war on another planet, due to her powers of premonition.
I should put something action-y here to round out the trio nicely, but I don't really watch any, so
Gurren Lagann? It's a very popular action show- great animation. A little too boob-happy for my tastes.