General:
* Opponent
* Enemy
* Foe
* Antagonist
* Competitor
* Contender
More specific:
* Rival (for a specific position or goal)
* Nemesis (a powerful and recurring enemy)
* Protagonist (in a story, the adversary of the main character)
* Accuser (in a legal context)
* Opponent (in a debate or argument)
The best synonym will depend on the specific meaning you want to convey.