The Caesars of the New Testament period:

Julio-Claudians  
27 BC -- 14AD Augustus (Caius Julius Caesar Octavianus), the adopted son of Julius Caesar, and the first emperor. After the assassination of Julius Caesar, Augustus fought five civil wars in order to avenge the death of Caesar, bring peace to the land, and make himself emperor.

Augustus married Livia after forcing her to divorce her first husband, and then adopted her son Tiberius. He initiated agressive urban renewal projects, built new temples and public forums, and generally made Rome into a prestigious capitol city. Augustus was a firm, conservative ruler who helped usher the golden age of the Roman Empire. He died at the age of 75--some say of natural causes, others that he was poisoned by Livia so that her son could be emperor. Both Augustus and Livia were deified posthumously.

14 -- 37 AD Tiberius (Tiberius Claudius Nero), son of Livia by her first marriage, and stepson to Augustus. Tiberius' brother, Nero Claudius Drusus, is the grandfather of Caligula and the father of Claudius. Tiberius had a great military mind but was not entirely comfortable as an administrator. He also had many vices. The last 11 years of his reign were spent on the island of Capreae in a sort of self-imposed exile where he reputedly practiced many moral depravities. Some say he died a natural death, others that he was poisoned by Caligula.  Tiberias was the Caesar during most of Jesus' 33 years.
37--41 AD Caligula (Caius Caesar), Tiberius' nephew and successor. As a small boy, Caius was very popular with the army because he was the son of their hero Germanicus, and because he often wore a miniature army uniform (the name Caligula comes from the word caliga, meaning small boot). Once he became emperor, however, Caligula quickly followed his great-uncle in moral scandal, had himself deified, killed a lot of people, and was eventually murdered by part of the Praetorian Guard.
41 -- 54 AD Claudius (Tiberius Claudius Drusus), Caligula's uncle. He was inflicted with some sort of paralysis at birth that left parts of his body stunted and his speech unlcear. He was a knowledgeable historian, and was not half-witted, as was commonly believed. Upon Caligula's death, Claudius was elected emperor by the Praetorian Guard (a rather unconstitutional move that was later emulated by several emperors). He eventually married his niece Agrippina Junior and adopted her son Nero, the future emperor. He was poisoned, probably by his wife so that Nero could be emperor. Claudius was deified during his lifetime by the Britains, and posthumously by the Romans.
54 -- 68 AD Nero (born Lucius Domitius Ahenobarbus; changed to Nero Claudius Caesar Drusus Germanicus when he was adopted by Claudius). Nero started as a just ruler but eventually gave himself to great excesses and bled the treasury dry. He started the great fire of Rome that destroyed nearly one-half of the city; then blamed it on the Christians, and cruelly killed thousands of them, including Peter, and Paul. He used some of the newly vacant land to build his infamous, sprawling Domus Aureus. He considered himself an artist, and gradually disregarded his duties as emperor in favor of touring as a professional singer. Eventually several provinces revolted, Nero lost the support of the army, and while on the lam committed suicide.