I highly recommend Paprika. The premise is that scientists have created a device called the "DC," which allows people to go into other folks' dreams and record them. There are even prototypes for a portable version called the "DC Mini." The downside is that the prototypes lack an essential bit of programming that keeps the dreamers' mind from essentially being hacked... which makes it really bad when the DC Mini prototypes are stolen. It's a visually stunning movie, with gorgeous animation, but there is a scene with some pretty serious body horror toward the end.
I also recommend Tekkonkinkreet. It's about a pair of orphan delinquents named Kuro and Shiro, who together form the gang known as "the Cats," and rule the streets of Treasure Town, a city on the verge of collapse. Their hold on Treasure Town is threatened by the arrival of the yakuza, who along with their boss, Snake, plan to turn the city into a massive amusement park. Kuro and Shiro find their home and their very lives under threat from not only the yakuza, but from alien assassins dispatched by Snake... and throughout it all, a mysterious entity known as the Minotaur lurks, its intentions unclear.