General movement:
* Shift
* Travel
* Transfer
* Relocate
* Transpose
* Change position
* Go
* Proceed
Emotional response:
* Touch
* Affect
* Inspire
* Motivate
Actions:
* Act
* Do
* Perform
* Operate
* Execute
Change of residence:
* Relocate
* Migrate
* Transplant
Chess:
* Advance
* Maneuver
For a specific example, please tell me what you're trying to say, and I can give you a more precise synonym.