It's claimed all the time by apologists that the writers of the New Testament were eye-witnesses to Jesus (particularly the gospel writers), but this simply isn't the case.
It is generally accepted that Mark is the earliest gospel written, and just who is Mark? He is believed to be a follower of Peter from the Gospel accounts, the rock upon whom Jesus apparently built his church. Did Mark ever meet Jesus? As far as we know he never knew the man at all. Matthew and Luke both used Mark as a source material for their gospels (although they contradict each other quite substantially concerning the birth narrative of Jesus, which Mark never mentions), and John is generally held to have been written in the very late first century or early second century. Considering that life expentancy in those days was ~40, and Jesus supposedly died around 29-33 C.E. By the time the gospels were written not a single one of Jesus' followers would still have been alive. Mark is placed around 70 C.E. at the earliest, So assuming Jesus' followers were at least teenagers during his ministry years, that would make them at least about 20 years old when he died. Add on another 40 years minimum to the writing of Mark, and that would make the youngest followers at least 60, which is rather unlikely considering the circumstances. If we're fairly certain that the youngest gospel was written by someone who wasn't an eyewitness, and that all eyewitnesses were likely to be dead by the time he put his pen to the paper, I think it is fairly safe to assume that the gospel accounts are unreliable.
EDIT: Sorry, I had the Life Expectancy wrong, it was 35 in the bronze/iron age not 40.