A recent study showed that more than 90% of depositions of the crucifixion show Jesus with his head turned toward the right, showing the left side of his face. The investigators speculate that artists are betraying an implicit understanding of the neuroscience of emotion — it is generally acknowledged that the left side of the face is more expressive, controlled as it is by the right cerebral hemisphere. However, there are plenty of non-neurological explanations:

‘For one thing, Mary is usually located to Jesus’ right, so maybe he is looking toward her. Or if Jesus is feeling abandoned by God, perhaps he is looking to the right, away from God (Jesus is usually described as being on God’s right-hand side). The saved are also depicted by convention on the right, so Jesus could be looking toward salvation. The number of speculations are almost endless.’ (Wired Science).