This question probably needs to be deconstructed a bit in order to fully answer it. Jesus, a given name, is the English transliteration of the Greek version of the personal name, which in Hebrew is Yeshua or, as we have it English, Joshua. (Jesus' name comes to us from the Greek because the New Testament was originally written in Greek. In the first-century and second-century, people who lived, traded, taught, studied, or governed around the Mediterranean basin used Greek either as their first or second language. Greek was to that world then what English is to much of the world today.)
Jesus is a name that means God saves and was, of course, also the name of Moses' successor in Old Testament times. The name of the man we Christians confess to be "true God and true man," as well as Savior of the world, was commonly known by His contemporaries as Yeshua bar Yosef: Joshua, son of Joseph.
Speaking of confession, the term of Christ attached to Jesus' Name is just that: a confession of faith about Jesus' identity and function. We Christians believe that Jesus, son of Joseph is the Christ.
Christ, christos in the Greek, translates a term from the Old Testament Hebrew, Messiah. Both words can be rendered as Anointed One in English.
In Old Testament times, the kings of God's people were anointed with oil during their enthronement ceremonies. Anointing was a sign of God's blessing as these leaders took on their responsibilities. Over time, prophets began to say that one day there would be a great King of kings, a Savior, to whom was commonly ascribed this title of Christ or Messiah.
According to the New Testament, when Peter confessed that Jesus was the Christ for the first time, Jesus affirmed Peter in that belief. (Although He subsequently chastised the impulsive disciple when Peter tried to rebuke Jesus for saying that He, as Messiah, would only fully reign after He had died on a cross and risen from the dead.) [See here.]
Now, did Jesus exist? Frankly, assertions that Jesus didn't exist are akin to claims that the Holocaust didn't happen.
A few examples of the evidence for Jesus' existence has recently been well-summarized by editors of the recently-published Archeological Study Bible.
- One ancient text, the Babylonian Talmud, speaks of Jesus being "hanged" on the eve of the Jewish Passover.
- The ancient Jewish historian, Josephus, in a document written by 93AD, has a description of an event he claims happened during the period when Pontius Pilate was governor of Judea. (It should be pointed out that Josephus was not a Christian):
"At this time Jesus, a wise man (if it is appropriate to call him a man), appeared. For he was a worker of incredible deeds, a teacher of men who happily receive the truth, and he drew to himself many Jews--and many Greeks too. [The term, Greeks, was used not just of those who were from Greece, but of Hellenized Jews or of non-Jews, Gentiles.] This man was the Christ. And when Pilate had executed him at the instigation of the leading men among us, those who had first loved him did not give up. For he appeared to them on the third day alive again..."
- In a later text, Josephus mentions the martyrdom of James, "the brother of Jesus, called Christ."
- In a document from the year 120AD, Suetonius mentions a riot in Rome that happened during the reign of the Emperor Claudius in 49AD. They were instigated, he said, by someone they called Chrestus.
- In 115, the Roman historian Tacitus decries the unjust execution of Christians by the Emperor Nero and talks about the term Christian. "The author of this name," Tacitus explains, "Christ, suffered the ultimate penalty at the hands of the procurator Pontius Pilate during the imperium of Tiberius."
The contemporary Jewish scholar Pinchas Lapide--like the ancient Josephus, not a Christian--has examined all of the evidence and concluded not only that Jesus existed, but that He rose from the dead. Why? Because of commitment and fearlessness seen in Jesus' first followers after Jesus had been killed on the cross.
This only makes sense. A conspiracy to support fabrications about the existence of a Savior Who both died and rose, a conspiracy involving at least 500 people--the number the New Testament says saw the resurrected Jesus--could not have been sustained in the face of rejection, persecution, and death threats unless Jesus was real and He really rose.
Did Jesus Christ exist? Absolutely! And I believe that He still does.
[Thanks to Andrew Jackson of SmartChristian.com for linking to this piece.]