There seems to be consensus among scholars that Jesus did in fact exist, but the difficulty lies in determining which Jesus everyone is talking about. To put it another way, it is plausible that there was more than one historical Jesus. To determine the historicity of Jesus, we look therefore at the ancients who mentioned him in their writings.
There are no accounts of Jesus written during his lifetime. The documents which have been collected as the Christian gospels were written after the fact. However, various unrelated writers such as Paul (the Christian saint), Josephus, and Tacitus mention Jesus to a greater or lesser extent. In his epistles, Paul discusses Jesus' crucifixion in an account that seems to correspond with some writings of Josephus. However, Josephus also writes about an incident involving James, "the brother of Jesus, who was called Christ" as follows:
Festus was now dead, and Albinus was but upon the road; so he assembled the sanhedrim of judges, 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: but as for those who seemed the most equitable of the citizens, and such as were the most uneasy at the breach of the laws, they disliked what was done; they also sent to the king [Agrippa], desiring him to send to Ananus that he should act so no more, for that what he had already done was not to be justified. (Josephus, Antiquities of the Jews, Book 20, Chapter 9)
The text goes on to state that Jesus, "son of Damneus," was subsequently made High Priest. It is safe to say that this passage is not in agreement with Christian writings. It has been speculated that this specific passage contains a marginal insertion added by a third party after the fact, specifically, "who was called Christ," and that Josephus was writing about another individual named Jesus in this particular passage.
Tacitus was a Roman Senator and historian, and his one-page mention of Jesus is frequently cited as independent Roman confirmation of the existence and crucifixion of Jesus:
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 Judæa, 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. (Tacitus, Annals, Book 15, Chapter 44)
This account would seem to match the gospel accounts of Jesus' conviction and death. Note, the Annals of Tacitus were written around AD 116, which would postdate the Pauline Epistles, written around AD 59, as well as the writings of Josephus, which were written around AD 93-94.
So while accounts of an historical Jesus do exist, they were written at a fairly great remove in time from the actual life of the Jesus spoken of in the gospels. For this reason, while many of the details about Jesus in these writings are in concert, the finer details differ. It is safe to say that the later writers such as Paul, Josephus, and Tacitus who mentioned Jesus were unable to verify their information with first person witness accounts.
So to answer your question: yes, it is fairly certain that a Jesus existed. The specifics of who he was, however, are a matter of scholarly debate or, if you are so inclined, of faith.