This is an interesting question. There are two days that are very important for Julius Caesar. And depending on who you ask, they will say that one of these days is Julius Caesar's day.
The first day is his date of birth - July 12, 100 B.C. This is an important day in Roman history because Julius Caesar is a transitional figure in Rome's history. He is the one who transformed the Roman Republic to an Empire. He also was a great general who conquered the Gauls and Pompey the Great.
The other day that is important (and more famous) is the Ides of March in 44 B.C. This is when Caesar was murdered by conspirators. The chief conspirators were Brutus and Cassius.
In Roman history, the ides of March is the middle point of the month. The ides of March is March 15th. What makes this date even more famous is that (in Shakespeare's rendition of the story) there were many omens that this was an ominous day for Caesar. Caesar, of course, disregarded this date and the conspiracy was successful.