The three most influential events in the life of Julius Caesar are difficult to define with precision, as he had a long and storied career as a consul, general, and politician, all areas that could contribute numerous events to the question.
For the sake of brevity, we will focus on the latter options, as the events that occur later work best for this question. One event is the formation of the First Triumvirate with Pompey and Crassus in 60 B.C.E. This three pronged leadership grouping was designed to consolidate power in Roman politics and eliminate the bureaucratic squabbling, that had dominated Rome since the time of Marius and Sulla. This was thought of as a time when men of great talent and influence could and would control the Roman world, and not always for the best of the city.
The Triumvirate controlled Roman politics until Crassus, the richest man in Rome, sought greater military glory in Parthia and ended up being defeated by Surena and killed. Crassus had been a close ally of Caesar and his influence kept the ambition of Pompey in check, who was jealous of Caesar's great success in the Gallic Wars. Pompey had also distrusted Crassus due to the Third Servile War against Spartacus, so he was subsequently suspicious of any of Crassus' friends. This naturally set the two former allies on the path to confrontation, which would start the Roman Civil War.
The second was Caesar's great success in the Gallic Wars of 58-50 B.C.E. mentioned above, as it brought him the necessary glory in the battlefield as part of the Cursus Honorum and enabled further political aspirations and support for his influence. His victories against the Gauls and their leader Vercingetroix were accomplished not through superior numbers, but through strategy built from his fore bearers such as Hannibal and Scipio Africanus. This was expertly demonstrated with the walled investment strategy at the Battle of Alesia. These victories brought Caesar great acclaim, culminating in a Triumph in Rome in which Vercingetorix was paraded in chains and then publicly executed. Much as we do in today's world, Rome loved a winner.
The third was his crossing of the Rubicon and subsequent victory in the civil war against Pompey that led to his sole rule of Rome as dictator in perpetuity. He was very popular with the Roman public due to his support for games in the Circus Maximus, ensuring that the "mob" of Rome would favor his sole rule. This did not naturally go over well with the Senate and the Optimates, so while this event was perhaps his greatest triumph, it also led to his untimely end of the Ides of March, 44 B.C.E. He was assassinated in the Senate by conspirators including his friend Brutus. The Senators justified his death as they feared that he would bring a return to Roman monarchy, which had been hated as a symbol of foreign Etruscan rule, which Rome could never abide to have again.