Is there evidence of Jesus outside of the Bible?

Yes.  Not only is there evidence of Jesus outside of the Bible but some of that evidence comes from hostile sources.  These are individuals or groups of people who were not writing to corroborate the historicity of Jesus but to demean the followers of Jesus.  Their remarks serve as nonbiblical corroboration of the veracity of Scripture.  For example…

 Josephus, Jewish historian, AD 37-100, described Jesus in his work, The Antiquities of the Jews. 

 “At this time there was a wise man who was called Jesus.  His conduct was good, and he was known to be virtuous. And many people from among the Jews and the other nations became his disciples.  Pilate condemned him to be crucified and to die.  And those who had become his disciples did not abandon his discipleship.  They reported that he had appeared to them three days after his crucifixion and that he was alive; accordingly, he was perhaps the Messiah concerning whom the prophets have recounted wonders.”

Tacitus, Roman historian, AD 56-117, referred to Jesus and to Christians in his work, Annals.  From a section in which he described Emporer Nero’s response to the great fire in Rome:

“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 and of one of our procurators, Pontius Pilatus, and a most mischievous superstition, thus checked for the moments, again broke out not only in Judaea, 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.” 

As we compile the description from the ancient writers outside of the Bible, we find a description of Jesus that matches the Biblical record.  Josephus, Tacitus, Thallus, Phlegon and Mara Bar-Serapion mention these things about Jesus:

He lived in Judea
A virtuous man
Had wondrous power
Could predict the future
Was the “Wise King” of the Jews
Accused by Jewish leaders
Crucified by Pilate
During reign of Tiberius
Darkness and earthquake at his death
Reportedly raised from the dead
Believed to be the Messiah
Called the Christ
Followers called Christian
A “superstition” about him spread

For further reading: Cold-Case Christianity, J. Warner Wallace