I think that most recent American animation has some noticeable anime influences in it...it's all just part of anime becoming more well-known, which has its pros and cons.
I'm a big fan of Batman: The Animated Series, but a lot of that is just nostalgia. That series focused a lot more on Batman being Batman, and very little on the character of Bruce Wayne. Which is one of the reasons I enjoyed Batman Beyond and Batman Begins. (Even my Dad liked Batman Begins. Score!)
And I loved the Joker's character in Return of the Joker. He always has been an interesting and unique villian, even compared to villians from other comic series. I was always a big fan of Harley, too.
("SWEETIE! Get Mommy her bazooka, kay?")
I'm actually a huge Marvel fan, but Batman is just the coolness. My old friend used to hide tons of Batman comics under her mattress so her parents wouldn't confiscate them.