Did Jesus of Nazareth really exist? Many would try to advocate the 'Christ Myth' theory, that Jesus never existed while others would argue that Jesus was a copy cat of pagan deities like Osiris, or Mithra as the Zeitgeist video tries to argue. Serious historians and scholars repudiate these ideas.
Even Bart Ehrman felt compelled to expose such 'Christ Myth' advocates that he wrote a book on the subject, Did Jesus Exist? The Historical Argument for Jesus of Nazareth (San Francisco: HarperCollins, 2012). What relevance does this have to Islam? Muslims tell us that the Qur'an portrays the perfect and pure record of Jesus and his teachings and that the New Testament cannot be trusted as it has been "corrupted". The major problem here is that the New Testament documents including the gospels are the earliest historical documents or biographies on Jesus written in the first century A.D. based on eyewitness testimony (Luke 1:1-4; John 19:35; 2 Peter 1:16; 1 John 1:1). The gospels were written a few decades after Jesus. The Qur'an on the other hand, comes 600 years later and borrows predominantly from apocryphal sources, folklore, and Jewish traditions. The Qur'an even implies this (Q 25:4-6). The earliest biography of Muhammad is believed to have been written by Ibn Ishaq (d. 767 A.D.) almost 150 years after Muhammad's death, but this biography does not exist in any extant copies but only in the heavily edited version of Ibn Hisham (d. 833 A.D.) which is 200 years after Muhammad's death. Most scholars believe that the earliest biography of Muhammad is actually that of al-Waqidi (d. 822 A.D.) Kitab al-Tarikh wa al-Maghazi ("The Book of History and Campaigns") which is almost 200 years after Muhammad's death. The Hadith of both Bukhari and Muslim are also over 200 years too late. The earliest, and thus most reliable historical sources for the life of Jesus and His teachings are the gospels themselves, not the Islamic texts.
Professor Stephen J. Shoemaker of the University of Oregon, who specializes in early Islam and Christianity, has openly admitted this important fact:
"the early biographies of Muhammad, the sira traditions...are not at all equal in their historical quality to the canonical Christian gospels...Despite frequent assertions to the contrary, our historical knowledge concerning Muhammad and first-century Islam is far more limited and uncertain than is the case with respect to Jesus and first-century Christianity." (Stephen J. Shoemaker, The Death of a Prophet: The End of Muhammad's Life and Beginnings of Islam (Philadelphia: University of Pennsylvania Press, 2012), p. 273.