How can I transfer my data to a new xbox 360?

Downloadable content should be able to be redownloaded at will, so you shouldn't have any issues there.

For your other content, such as saved games, movies, etc., you have a couple of options:

1. The XBox 360 hard drive transfer kit, if you have one around.
2. If the content is sufficiently small, you can use memory cards, manually moving the data onto the cards, then onto the target XBox.
3. If the content is larger, you can use up to 16GB of USB-based memory now. So a 16GB flash drive can be recognized for store-purchased, as well as in-game (saves, etc.), data.

Once the data is transferred, you will also want to transfer your licenses for content. Instructions are available on the xbox 360 site.