Formal:
* Bough: A large branch of a tree, especially one that grows out horizontally.
* Branch: A part of a tree that grows out from the trunk or another branch.
* Twig: A small branch of a tree.
Informal:
* Arm: This is a more informal way to refer to a tree limb.
* Shoot: This is a term often used for a young, fast-growing branch.
The best word to use will depend on the context. For example, if you are writing a formal report, you might use the word "bough". If you are talking to a friend, you might use the word "arm".