Some artists, especially during the Renaissance, depicted Jesus with red hair. Why? Well, 1 Samuel 16:12 says that Jesus' great-great-great-great- great-great-great-great- great-great-great-great- great-great-great-great- great-great-great-great- great-great-great-great- great-grandfather David was "ruddy." However, the text seems to be describing a reddish tone to David's skin, and to claim that this text meant that David's distant relative had red hair is pretty far-fetched. Others have argued that Jesus had woolly hair by citing Revelation 1:14. Besides the fact that this is Apocalyptic literature, which is notoriously difficult to use in arguments about a person's physical appearance, the entire passage reads as follows:
"His head and his hair were white as white wool, white as snow."
The point is not that Jesus' hair had the texture of wool, but that in this Apocalyptic appearance, Jesus' hair was radiant, in order to emphasize his glory and power.
So then, in reality what did Jesus look like? Well, some scientists for a BBC special measured several skulls of middle aged Jewish men from Roman period Palestine, and they put together a composite of what the average man might have looked like at that time. And this is what they came up with.
Image from BBC
Not at all the traditional image of Jesus with a long face, as this idea developed hundreds of years after Jesus.