General Words
* Counteract: To act against or neutralize the effects of something.
* Counterbalance: To balance or offset something with something else.
* Counterclaim: A claim made in response to an opposing claim.
* Counterfeit: An imitation made to deceive; fake.
* Counterintuitive: Contrary to what intuition would suggest.
* Countermand: To cancel or revoke an order.
* Counterproductive: Having the opposite of the desired effect.
* Counterproposal: A proposal made in response to another proposal.
* Counterrevolution: A movement that opposes a revolution.
* Countersign: To add one's signature to a document already signed by someone else.
More Specific Words
* Counterargument: An argument that opposes another argument.
* Counterattack: An attack in response to an attack.
* Counterclockwise: In a direction opposite to the movement of the hands of a clock.
* Counterculture: A culture whose values and practices are in opposition to the mainstream culture.
* Counterintelligence: Intelligence activities aimed at countering the intelligence activities of an enemy.
* Countermeasure: An action taken to prevent or minimize the effects of something.
* Counterpart: A person or thing that has the same function or position as another.
* Counterexample: An example that contradicts a general statement.
* Counterterrorism: Measures taken to prevent or combat terrorism.
This is not an exhaustive list, but it gives you a good starting point for words that begin with the prefix "counter-."