General:
* Associate
* Colleague
* Comrade
* Fellow
* Friend
* Spouse (in a romantic context)
In Business:
* Associate
* Collaborator
* Co-worker
* Joint venturer
* Teammate
* Business associate
In a Relationship:
* Spouse
* Lover
* Significant other
* Sweetheart
* Boyfriend/Girlfriend
In Dance or Sports:
* Teammate
* Co-player
* Dance partner
* Running mate
In Crime:
* Accomplice
* Conspirator
* Co-conspirator
The best synonym for "partner" will depend on the specific situation and the relationship between the people involved.