Jesus is the central figure of the Christian faith and as such he is quite "real" to Christians. Members of the Islamic faith also revere Jesus as a genuine prophet of God. (They do not recognise Christ as the "Son of God", however).
However the question of whether or not there was genuine, historical human being behind the Biblical stories and the religious belief is a matter that has been widely debated over the past few hundred years.
At the present time the general academic consensus is "Yes, Jesus did exist".
There has been extensive analysis by scholars of both religious documents and secular records from the time period. As a result it is now generally accepted that there really was a Jewish teacher named Jesus (or to use the Hebrew form, "Yeshua") who came from Galilee during the time period claimed in the Bible. Additionally it is generally accepted by scholars that this Yeshua was regarded as a healer by the local population, he was baptised by John the Baptist, he was accused of sedition against the Roman Empire, and he was sentenced to death by crucifixion on the orders of the Roman Governor Pontius Pilate.
The remainder of the details, such as whether or not Jesus was born of a "virgin birth", performed numerous miracles, and was resurrected after his death is largely a matter of personal faith. There is no objective evidence apart from the Biblical stories to prove it to be true, neither is there anything to conclusively prove it false.
It is known that some of the details about Jesus are remarkably similar to older stories from other religions and mythology. For example the Hindu god Shiva was born in a manger and at his birth he was visited by wise men from the east. Some have used these similarities to argue that the entire existence of Jesus has been fabricated.
However this does not definitively rule out the existence of Jesus as a person. While accepting that the Biblical story of Jesus may not be absolutely factual, the academic James Charlesworth writes "No reputable scholar today questions that a Jew named Jesus son of Joseph lived".
For more information see Wikipedia's entry on the Historicity of Jesus