General words:
* Contrary: Opposite in nature, character, or direction.
* Contradict: To assert the opposite of something.
* Contrast: The state of being different or opposite.
* Contrapuntal: Relating to counterpoint in music, where melodies are played simultaneously.
* Countermand: To cancel or revoke a previous order.
* Counterfeit: Imitation, especially with the intent to deceive.
* Counterproductive: Having the opposite effect of what was intended.
* Counterrevolution: A movement to overthrow a revolution.
Scientific/technical:
* Contraindication: A reason why a particular treatment should not be used.
* Contraception: The prevention of pregnancy.
* Contravene: To violate or infringe upon.
* Contractible: Able to be contracted or shortened.
Other words:
* Contraband: Goods that are prohibited from being imported or exported.
* Counterclockwise: In a direction opposite to the movement of the hands on a clock.
* Counterpart: A person or thing that has the same function or position as another.
* Counterbalance: To balance something by putting something opposite it.
* Counterpoise: To balance by opposing forces.
* Countersign: To sign a document in addition to someone else.
This is not an exhaustive list, but it gives you a good idea of the range of words that can be formed from the root "contra."