General:
* Create
* Write
* Form
* Construct
* Make
* Draft
* Frame
* Put together
* Assemble
* Devise
For music:
* Score
* Set
* Arrange
* Orchestrate
For writing:
* Author
* Pen
* Craft
* Produce
For other things:
* Organize
* Arrange
* Constitute
* Establish
* Settle
The best synonym will depend on the specific situation. For example, if you're talking about writing a letter, "compose" and "write" are interchangeable. However, if you're talking about putting together a puzzle, "compose" might not be the best word to use.