I looked into the debate over the historicity of Jesus a few years back so any information I have now is based mostly on the information available then. I'm not sure if anything has really changed or if any significant and new information is available.
A few things to keep in mind when examining this topic matter:
1. First and foremost I think it's important to note the status of Jesus during that time period in the Levant and outlining areas. He was more or less a nobody outside of his small group of people, he became posthumously famous.
2. Written language was not the same then as it is today, people didn't carry around a pen and paper (so to speak) and write things down that they found noteworthy. Oral tradition was the main way that important information was retained and then passed on to succeeding generations.
3. History is not scrutinized in the same way that science is with the scientific method, they're in different fields of study and in the social sciences different methods are used including a process to analyze the accuracy of oral tradition.
One of the main sources cited when it comes to the historicity of Jesus (outside of the bible itself) is Josephus (
Antiquities of the Jews). This source has been heavily scrutinized and for a good reason, a significant portion of the writing that goes into detail on Jesus is now accepted by many as an insertion made later on by Christian scribes.
They wrote:
3. Now there was about this time Jesus, a wise man, if it be lawful to call him a man; for he was a doer of wonderful works, a teacher of such men as receive the truth with pleasure. He drew over to him both many of the Jews and many of the Gentiles. He was [the] Christ. And when Pilate, at the suggestion of the principal men amongst us, had condemned him to the cross, (9) those that loved him at the first did not forsake him; for he appeared to them alive again the third day; (10) as the divine prophets had foretold these and ten thousand other wonderful things concerning him. And the tribe of Christians, so named from him, are not extinct at this day.
http://www.sacred-texts.com/jud/josephus/ant-18.htm
I think it's important to note that the placement of the above paragraph is semi-significant. It makes it much more likely that they (christian scribes) were simply embellishing on what was already written by Josephus since ordering in their culture was important and they would have likely placed that paragraph somewhere after John the Baptist (it's the logical succession of the story). There's also a brief mentioning of Jesus in a later chapter that's much less descriptive which is not considered a later addition.
and brought before them the brother of Jesus, who was called Christ, whose name was James, and some others, [or, some of his companions]; and when he had formed an accusation against them as breakers of the law, he delivered them to be stoned:
http://www.sacred-texts.com/jud/josephus/ant-20.htm
Also important to note is the authenticity of the first paragraph is still debated by scholars over whether or not it was completely written by christian scribes, if just part of it was, or if none of it was. They say that the writing style was identical to Josephus and that it is included in all manuscripts however the description of Christ given is not what you would see being used by someone who was Jewish.
Next we have Tacitus who mentions Christus (Annals 15(44):
Consequently, to get rid of the report, Nero fastened the guilt and inflicted the most exquisite tortures on a class hated for their abominations, called Christians by the populace. Christus, from whom the name had its origin, suffered the extreme penalty during the reign of Tiberius at the hands of one of our procurators, Pontius Pilatus, and a most mischievous superstition, thus checked for the moment, again broke out not only in Judaea, the first source of the evil, but even in Rome, where all things hideous and shameful from every part of the world find their centre 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. Mockery of every sort was added to their deaths.
Tacitus: Annals: Book 15 [40]
For those of you who are not familiar with Tacitus he was a Roman historian in the middle of the 1st century, some scholars question the authenticity of this passage but not too many do given it's tone and the way this Christus character and his followers were portrayed.
There's more mention of Jesus in writings outside of the bible, I just put down the two most noteworthy sources for you all to check out. Personally I think evidence for the existence of Jesus (the one in the bible), fits in with textual and oral historical methodologies. He is written about by multiple sources and the amount he is written about is consistent with the fact that he was not a major figure of the time, his life may have been worthy of jotting down by a few historical figures but outside of his group of followers he was a fairly insignificant person from a historical perspective. There is no first hand account of his life outside of the bible but there is writings from historical figures that sort of mention him as a sideline figure. The more significant historical data comes from oral tradition.
In conclusion I think you can make a case for both sides but the historical Jesus is documented much more heavily than a lot of other "accepted" historical figures which makes me wonder why so many people are trying so enthusiastically to disprove his existence.
List of people to look into if anyone is interested (some are more heavily scrutinized then others so I suggest getting both sides of the story when examining each possible source):
Tacitus (54-119AD)
Suetonius (75-160AD)
Pliny the Younger (61-115Ad)
Philo (?- 40+AD)
Josephus (37-94AD contemporary of the apostles)
Then of course you have the writings of the bible as a source and the apocrypha.