In his Antiquities of the Jews at the end of the 1st century, Josephus, the Jewish historian, refers to Jesus as “a wise man, a doer of wonderful works” who “drew over to him both many of the Jews and many of the Gentiles” . . . . Tacitus, the Roman historian who lived from 55 to 120, mentions “Christus” in his Annals. In about 120 Suetonius, author of The Lives of the Caesars, says: “Since the Jews constantly made disturbances at the instigation of Chrestus, Emperor Claudius expelled them from Rome.”
All of the other sources derive from the church itself. A colllection of essays on the topic from a secular perspective are found here.
Much of the New Testament in the Christian Bible is attributed to Paul, whose conversion to Christianity followed the crucifixion. In other words, Paul was not a contemporary of Jesus. Yet, Paul's writings are actually the earliest of the New Testament canon, containing epistles that precede the Gospels in order of composition. This is one of the reason that Paul's writings are given so much emphasis in fundamentalist Christianity which generally seeks to emulate "the early church" prior to the elaborations associated with organized Roman Catholic practice.
The canonical Gospels themselves are generally believed to have been written decades after the events that the describe (with the Gospel of John being the latest), and many historical biblical scholars believe that the Gospels contain many significant elaborations inserted for literary effect that go beyond earlier and more sparse sources that have been lost to the Biblical canon. The Gospels of Luke and Matthew were written about two decades after the Gospel of Mark, which is the earliest of the four canonical Gospels, and is believed to have been an important source for both later works by most mainstream biblical scholars. Mark itself may have been the product of one or two proto-Gospels, one of which is often referred to as a "sayings Gospel" and the other of which would have provided much of the narrative glue between those sayings. The few non-canonical religious sources that survive, despite systemic efforts to destroy non-canonical religious documents in the Roman Empire, provide tantalizing hints that the sayings gospel did indeed exist.
The relevance of this to the historical Jesus is two fold.
First, many of the additions of Luke and Matthew to Mark, such as the Christmas story and the accounts of the youth of Jesus (Chapters 1 and 2 of Matthew and Chapters 1 and 2 of Luke) are likely later elaborations. There is also strong historical evidence from early church scholars that the 9th to the 20th verses of the 16th Chapter of the Gospel of Mark, which recount events after the resurrection of Jesus, were editorially inserted by a much later author.
Second, the most plausible alternative to the Gospels is that someone like Paul simply invented Jesus, either out of whole cloth, or out of a minor historical figure who didn't do anything meaningfully like the story told in the Gospels, and that this proto-gospel (in connection with what might have been an independent collection of religious wisdom) later gave rise to the Gospel of Mark and other texts that make up the New Testament Canon. It is a common device for story tellers to attribute a story to someone else, relegating themselves to the mere role of a passive observer and playing a minor role in the larger story, so that their own personal credibility is not intertwined with the authority of the message that they are telling. The Roman world of the time was full of fantastic tales of figures similar to Jesus at the time (and early Christianity may very well have borrowed from some of those early Roman cults). Some credence is lent to this theory by the fact that there are no canonical or non-canonical historical documents which anyone credibly claims were written by Jesus himself, despite the claim of Chapter 2 of the Gospel of Luke that Jesus was far better acquainted with religious lore than his own upbringing in a carpenter's household should have made possible if he was illiterate.
Of course, everyone agrees that Christianity as a religion did come into existence sometime in the first couple of centuries C.E., that it grew in influence and organization (creating more and more documents,including the early Christian canon that eventually became the Christian Bible) and that by the early 300s, Emperor Constantine gave Christianity official recognition which continued in varied forms until the fall of the Roman Empire a couple of centuries later. Moreover, it is also undisputed that for the next one thousand years (sometimes known as the "dark ages") between the fall of the Roman Empire and the Italian Renaissance, that Christianity, particularly the monastic movements, played an important part in sustaining what remained of civilization after the empire's fall.
Furthermore, it is clear that the story of the Gospels was more important than any historical reality in the influence of the figure Jesus Christ, whether he was historical or merely an invented character, on the world. For example, the Islamic treatments of Jesus Christ almost certainly derive from the Christian religious account, modified by its own spin. It is even possible that the non-Christian historical sources mentioned above have as their source a fictional proto-Gospel invented by the biblical author whom we know as Paul, disseminated by early missionaries even before the Gospel of Mark was written.
Now, even if the Gospels do have a real historical Jesus Christ as their foundation, this doesn't necessarily mean a whole lot. The existence of a historical Jesus does not imply that this individual was God. Indeed, the nature of the divinity of Christ -- as a mere human prophet, as purely divine, as something in between or both (the predominant theological view now as a result of largely political gatherings of religous figures that gave rise to the creeds used by liturgical chuches today, such as the Nicene Creed), was a factor in political power struggles in the Roman empire and a source of dispute between different sects of Christians for centuries. There is some reason to believe that some of the most clear scriptural references to the divinity of Christ in the Bible are themselves reactions to these controversies, added after the fact, a claim adhered to by most Unitarian Christians past and present.
Religiously speaking, the existence of a historical Jesus is really secondary to the question of the existence of the Christian God as described in the Bible. A historical Jesus's existence is one of many relatively minor coroborating facts, none of which themselves is sufficient to prove the existence of God, which support the claim that the Bible is authentic, at least to a great extent.
Personally, I am agnostic on the existence of a historical Jesus. But, it is clear to me that the supernatural aspects of the Gospel stories, including a claimed divinity of Jesus Christ, are not true.