General:
* Hone
* Point
* Edge
* Refine
* Enhance
* Improve
* Polish
Specific to tools:
* Grind
* Whet
* Resharpen
Specific to mental abilities:
* Stimulate
* Activate
* Focus
* Concentrate
Specific to senses:
* Amplify
* Intensify
* Exacerbate
The best synonym for "sharpen" will depend on the specific situation and what you are trying to communicate.