Wow, this is a great thread! These wouldn't be my top 10, but probably fit the bill of artistic influence the best. I'm sure I'm forgetting a dozen or so. My two cents (in no particular order)
1) Spirited Away - Simply amazing. Not only for the character design and story, but for the use of subtlety in conveying character traits. The scene that stands out is in the furnace room when Chihiro is fiddling with her shoes... a subtlety that cost a fortune (in frames of animation) but does so much to speak to her apprehension and her insecurity, remaining a little girl in spite of her fantastic situation.
2) Nausicaa - Breathtaking, epic, and beautiful. Just pure perfection.
3) Akira - I don't know if anyone mentioned this one, but if not I'm surprised. This film is the single reason I am a big manga and anime fan today (and all the influences that those things have brought to my work). There was a rumor going around saying someone was going to make a live action remake of this, and one journalist nailed it on the head: "Why would you remake a movie that's already perfect?"
4) Memento - Absolutely original, and a wonderful introduction to a brilliant director.
5) Shaun of the Dead - Just brilliant, start to finish. The love for this project (Hot Fuzz as well) just pours out of every frame. If you can hunt down their tv show "Spaced" you should do so, also brilliant (starring Simon Pegg with Nick Frost cameos, directed by Edgar Wright).
6) Pan's Labyrinth - True fantasy played out on screen.
7) Tron - I know, it's corny. But if you asked my 8 year-old self, it was pure gold, and it gets the imagination spinning. Probably one of the first times I wanted to create characters and worlds in my head (and on paper).
Goonies - Same reasons as number 7. Pure high adventure.
9) Alice in Wonderland - Disney really took a risk with this one given their bread and butter. I think it's the reason I always want forests to have fantastic mushrooms and crooked tree stumps in them.
10) Sleepy Hollow - Not the best film Burton's ever done, but one of my favorite design wise. The town of sleepy hollow and the surrounding woods are characters in and of themselves.