"Suetonius was a secretary and historian to Hadrian, Emperor of Rome from 117 to 138 AD. Regarding Emperor Claudius (41-54 AD) and the Riot of Rome in 49 AD, Suetonius wrote:
As the Jews were making constant disturbances at the instigation of Chrestus [Christ], he [Claudius] expelled them from Rome.
Interestingly, Acts 18:2 relates that Paul met Aquila and his wife Priscilla just after they left Italy because Claudius had expelled them.
Later, Suetonius wrote about the great fire of Rome in 64 AD:
Punishment by Nero was inflicted on the Christians, a class of men given to a new and mischievous superstition.
Mara Bar-Serapion, a stoic philosopher from Syria, wrote this letter to his son from prison sometime after 70 AD:
What advantage did the Athenians gain from putting Socrates to death? Famine and plague came upon them as a judgment for their crime. What advantage did the men of Samos gain from burning Pythagoras? In a moment their land was covered with sand. What advantage did the Jews gain from their executing their wise king? It was just after that that their kingdom was abolished. God justly avenged these three wise men: The Athenians died of hunger; the Samians were overwhelmed by the sea; the Jews, ruined and driven from their land, live in complete dispersion. But Socrates did not die for good; he lived on in the statue of Plato. Pythagoras did not die for good; he lived on in the statue of Hera. Nor did the wise king die for good; he lived on in the teaching which he had given.
This letter refers to Jesus as being the "wise king." The writer is obviously not a Christian because he places Jesus on an equal level with Socrates and Pythagoras. Without bias in his reference to Jesus and the church, this letter is a valuable historical reference regarding the historicity of Jesus.
Lucian of Samosata was a 2nd century Greek philosopher. This preserved text is obviously satirical, but it's a powerful "extra-biblical source":
The Christians, you know, worship a man to this day -- the distinguished personage who introduced their novel rites, and was crucified on that account... You see, these misguided creatures started with the general conviction that they are immortal for all time, which explains the contempt of death and voluntary self-devotion which are so common among them; and then it was impressed them by their original lawgiver that they are all brothers, from the moment that they are converted, and deny the gods of Greece, and worship the crucified sage, and live after his laws. All this they take quite on faith, with the result that they despise all worldly goods alike, regarding them merely as common property.
This piece is unflattering at best, but it absolutely supports the person of Jesus Christ ("the crucified sage") and the survival of the Christian Church into the second century."