In addition to the death of Caesar, you might say that the deaths of other characters were noble. Brutus went along with the assassination of Caesar because he truly believe it was best for Rome. He didn't want to kill his friend, but felt he needed to. Toward the end of the play, Brutus takes his own life because he knows he has lost and many of his men have died (many by taking their own lives). When Antony finds him dead, he proclaims that Brutus is the most noble man he ever knew. Calling Brutus noble most definitely makes his death seem noble.
Caesar’s death was also considered noble because he lived his life nobly and died nobly. To live one’s life nobly is hard enough, but to die nobly is no mean feat. This is especially true considering that he was betrayed by his supposed honorable nobles. He contrasts their apparent nobility with his true nobility.
Antony is also able to ennoble Caesar by using his dead body. He gains sympathy from the mob by pointing to the stab wounds and the bloody cloak. On the other hand, his speech claims that the "evil that men do lives after them;/The good is oft interr'd with their bones," suggesting that death is not ennobling for some people. But overall, death, particularly death rather than submission, is portrayed as noble. Brutus's death is framed as the act of a truly noble Roman--indeed, Antony reflects that he was the noblest of them all.
Some people look at the way Caesar died and consider it noble. It took over 30 stabs to kill him--he didn't die easily, and he faced Brutus at the end with the words "Et tu Brute."
A number of the characters commit suicide in the play. In their minds it was more noble to end their own lives than to live in the bondage that would have followed had they survived. Brutus and Cassius were not willing to live as Caesar's slaves, so they took their own lives.