Contemporary or near contemporary extra-biblical evidence for the existence of Jesus is thin. It consists of the following:
1) In the Annals of Imperial Rome, written probably early in the second century, Tacitus says that Jesus was put to death by Pontius Pilate for sedition. Since the Annals were written nearly a century after any historical Jesus would have died, this could be second-hand hearsay, Tacitus merely repeating what Christians said of Jesus. However, one can invoke the criterion of embarrassment, i.e. that saying your savior was a felon sentenced to death for sedition isn't something early Christians would have made up about Jesus.
Beyond that, all we have are two mentions of Jesus in Antiquities of the Jews by Josephus. One of these, the Testamentum Flavianum or, simply, the "Testimonial," which asserts Jesus was the Christ, is clearly an inserted forgery. The other, referring to the execution of James, calls him the brother of "Jesus who was called the Christ." While this could merely mean that Jesus was alleged to be the Christ, the "who was called the Christ" phrase may have been added by a later editor. Considering that Jesus (Yeshua) was an extremely common name - there are eight of them in the Antiquities, if "who was called the Christ" was a forged by an editor, we have no evidence from Josephus. This, however, could merely mean that, whoever Jesus was, he lacked the status of, say, John the Baptist.
The only contemporary evidence beyond that for the existence of Jesus are inferences from the gospels involving the criteria of embarrassment and difficulty. For example, if one was making up Jesus out of whole cloth, and he was supposed to be born in Bethlehem, then one would simply have him come from Bethlehem; end of story. However, the Gospels of Matthew and Luke go through elaborate contortions to generate the fiction that Jesus, though he came from Galilee, actually originally was born in Bethlehem, that it seem they were stuck with a real guy who came from Galilee. this would be a difficulty if one is trying to pass said messianic pretender off as the Messiah, when Micah 5:2 prophesied the Messiah would come from Bethlehem, the hometown of David.
Personally, I think that Jesus really did exist. He was probably influenced by the prophetic tradition, along with Cynic philosophy and Jewish messianism. I see him as a failed messianic pretender who was arrested for treason - possibly with his own complicity, since he actually expected to rise from the dead - and put to death.
Whether or not Jesus was historical may, in fact, be moot. Paul, the real founder of the Christian religion, simply dispenses with any historical Jesus in his epistle to the Galatians:
(Gal. 1:11, 12, emphasis added): For I would have you know, brethren, that the gospel which was preached by me was not man's gospel For I did not receive it from man, nor was I taught it, but it came through a revelation of Jesus Christ.
(Gal. 1:15 - 17, emphasis added): But when he who had set me apart before I was born, and had called me through his grace, was pleased to reveal his son to me, in order that I might preach him among the Gentiles, I did not confer with flesh and blood, nor did I go up to Jerusalem to those who were apostles before me, but I went away to Arabia; and again I returned to Damascus.
