Julius Caesar's enemies changed throughout his life. The most notable enemies at the time of his death in 44 B.C. were Marcus Junius Brutus (the addressee in Shakespeare's famous "Et tu, Brute?") and Gaius Cassius Longinus.
Caesar entered into a treaty with his long-time friend Gnaius Pompeius Magnus (Pompey) and Marcus Licinius Crassus in 60 B.C. This is known as the First Triumvirate, and it only lasted until the early 50's B.C. Pompey gradually turned on Caesar after the dissolution of the Triumvirate.
When Caesar crossed the Rubicon (the origin of the phrase "iacta alia est," or "the die is cast"), he made many enemies; a large portion of the Senate rebuked him for crossing the river. The disagreement over pro and anti-Caesarians began the Civil War. Pompey fled Rome at this time, fearing that Caesar was too strong of an enemy.
Cato the Younger became an enemy of Caesar's during the Civil War. Cato believed in a strict moral code and social severity, while Caesar spoke out for social reforms and a new system of government that moved power away from the senate. Cato fled Caesar and eventually killed himself, fearing Caesar's new political system and not wishing to be pardoned by his enemy.
Brutus was the most famous enemy of Caesar. Formerly a close ally of Caesar, Brutus secretly turned on him and is said to have begun the fatal attack on Caesar on the Ides of March (March 15, 44 B.C.).