It is quite difficult to know where to start, because actually the evidence for Jesus is so massive that, as a potential historian, I want to say we have got almost as much good evidence for Jesus as for anyone in the ancient world. Obviously there are some characters from the ancient world for whom we have statues and inscriptions. On the other and, we have statues of gods and goddesses in the ancient world too, and so you can never quite be sure. But in Jesus' case, the evidence all points firmly back to the existence of this great figure in the twenties through to around thirty of the first century.
And the evidence fits well with what we know of the Judaism of the period, even though much of it was eventually written down a generation later, that I think there are hardly any historians today, who doubt the existence of Jesus. There are one or two. A man called G.A. Wells is the only one who made much of it recently. From time to time you get someone like J.M. Allegro, who a generation ago wrote a book on the basis of the Dead Sea Scrolls saying that Christianity was all about a cult of sacred mushroom. No Jewish, Christian, atheist, or agnostic have ever taken seriously since. It is quite clear that in fact Jesus is very, very well documented character of real history. So I think that question can put to rest.
Sure, there are some self-proclaimed experts on the Internet who claimed Jesus never existed, but these aren't scholars with academic credentials. Only a very small handful of legitimate scholars, such as the skeptic Robert Price, suggests they wouldn't be surprised if Jesus never existed, but even Price falls short of asserting Jesus never lived.