In the Assassin's Creed series, the order that opposes the Assassins is the Templars.
The Templars are the principal antagonistic organization in the franchise. They generally seek peace through control, authority, and the use of powerful Pieces of Eden, while the Assassins defend individual freedom and resistance to imposed rule.
The rivalry is not limited to one historical period. Assassin's Creed uses the Animus to connect stories set in many eras, so versions of the conflict appear during the Crusades, the Renaissance, the American Revolution, the French Revolution, and other periods.
The series draws inspiration from the historical Knights Templar but presents a fictional secret organization that survives and changes over centuries. The Abstergo corporation serves as a modern-day continuation of Templar influence in the games' present-day storyline.