First, I would say that is is clear that folks from both sides of the debate have already arrived at their conclusion to the question. Let's not pretend to look for the "truth" and then attempt to debunk every post that presents evidence for the opposing viewpoint.
With that, the evidence:
Tacitus was a Roman historian writing early in the 2nd century A.D. His Annals provide us with a single reference to Jesus of considerable value. Rather frustratingly, much of his work has been lost, including a work which covers the years 29-32, where the trial of Jesus would have been had he recorded it. [Meie.MarJ, 89]
Here is a full quote of the cite of our concern, from Annals 15.44. Jesus and the Christians are mentioned in an account of how the Emperor Nero went after Christians in order to draw attention away from himself after Rome's fire of 64 AD:
But not all the relief that could come from man, not all the bounties that the prince could bestow, nor all the atonements which could be presented to the gods, availed to relieve Nero from the infamy of being believed to have ordered the conflagration, the fire of Rome. Hence to suppress the rumor, he falsely charged with the guilt, and punished Christians, who were hated for their enormities. Christus, the founder of the name, was put to death by Pontius Pilate, procurator of Judea in the reign of Tiberius: but the pernicious superstition, repressed for a time broke out again, not only through Judea, where the mischief originated, but through the city of Rome also, where all things hideous and shameful from every part of the world find their center and become popular. Accordingly, an arrest was first made of all who pleaded guilty; then, upon their information, an immense multitude was convicted, not so much of the crime of firing the city, as of hatred against mankind. From
http://www.tektonics.org/jesusexist/tacitus.html
Josephus:
Antiquities 20.9.1 But the younger Ananus who, as we said, received the high priesthood, was of a bold disposition and exceptionally daring; he followed the party of the Sadducees, who are severe in judgment above all the Jews, as we have already shown. As therefore Ananus was of such a disposition, he thought he had now a good opportunity, as Festus was now dead, and Albinus was still on the road; so he assembled a council of judges, and brought before it the brother of Jesus the so-called Christ, whose name was James, together with some others, and having accused them as law-breakers, he delivered them over to be stoned.
Also, let's think about the context in which Jesus lived.
1. He lived in a culture where most people were illiterate (but still smart!). Therefore there would not be an abundance of documents about him.
2. He was not one to dialogue with major historians or political figures of the time. In fact, his later followers received more attention than he did.
Finally, there are also several conversation between early Christians and non-Christians discussing whether Jesus was the Messiah. The question was if he was really the Son of God, not whether the man named Jesus actually existed. That was assumed by both.