Anime Movie with a floating island and robots
It's Laputa: Castle in the Sky.  The story starts off with a girl on a airship that's attacked by "sky" pirates. She manage to escape both the pirates and the people who held her captive on the airship by falling out of it. The girl's amulet saves her, causing her to float to safely to ground where a young boy find her.

Ultimately they end up on the floating island Laputa, which is old, overgrown, has a giant tree and is populated by giant robots. I believe the robots can fly.