General:
* Complete
* Done
* Over
* Ended
* Concluded
* Accomplished
* Completed
* Terminated
* Closed
* Through
* Finished with
More specific:
* For tasks or projects: Completed, accomplished, concluded, wrapped up
* For events: Ended, concluded, over, finished with
* For objects: Built, made, manufactured
* For food: Cooked, prepared, ready to eat
Informal:
* Donezo
* All done
* Finished up
* Through with
The best synonym will depend on the specific context and the nuance you want to convey.