To get things started, here are some examples of animations I find inspiring:
I can't talk about animations I look to for inspiration without mentioning anime. I grew up with it, and it's influenced me more than I can say. Anime can be limited in animation, but it focuses on aesthetic and design elements, which I find very important.
Dramatic storytelling isn't something I see often in mainstream American animation. To be marketable, films tend to be family friendly, simple in plot, and humorous. While the film itself wasn't a total success in this area, I still remember the chills I got watching this scene; it was dramatic, dark, mature, and different.
And for artsy film's sake, here is a part of this year's Oscar winner:
Again, this is film has a mature, heartfelt story with a strong visual style. It was successful without necessarily conforming to the Disney formula.