I love anime. The characters are expressive, constantly jumping and flailing about. The dialogue is completely random - possibly because something gets lost in the Japanese-to-English translation. The plots are so fantastic that a willing suspension of disbelief is not only helpful, it is necessary. I think it has to do with the manga/anime market in Japan - the audience is voracious, and is willing to read weird-ass stuff. The result is a lot of WTFery, but also a lot of awesomeness. Case in point: Sailor Moon.
Possibly one of the most well-known anime shows in the U.S., Sailor Moon was at the forefront of the Japanese cartoon invasion. It has something for everyone - short skirts and fighting for the boys, romance and badass chicks for the girls. Serena, the heroine of the show, is a below-average student, a goof ball, a klutz. She also has an enormous capacity to love and can vaporize baddies with a wave of her magic wand. Her pure heart inspires loyalty - she is the undisputed leader of the Sailor Scouts, even though everyone refers to her as "meatball head."
And okay, maybe a sexy superheroine who can't do math is not the best role-model for impressionable young girls. But I'm currently watching the third season, Sailor Moon Super, and was pleasantly surprised at the inclusion of a genderqueer character. Sailor Uranus (pronounced Ura-nis, plx kthx) always dresses in men's clothes when she's not on duty. She has "manly" hobbies and habits, and speaks in a deep voice. It's treated as something surprising but not freakish or wrong, and several of the other Sailor Scouts develop crushes on her masculine persona. Spoiler alert: though she and Sailor Neptune are billed as cousins in the English dubbing, everyone knows they are lesbian life-partners.