Although they never show his face in the games, he has made a couple of appearences without his armor as a child and as a teen in some of the novels. but no show in his current age.
I did see, once, a picture of a Spartan with the MJOLNIR MARK VI armor the Master Chief wore with the helmet off, but it showed nothing but his back and the back of his head, which was shaved of course. There were UNSC ships launching in the background, and he was looking over them. Of course, this could have been fan art, but I somewhat doubt it because of the amazing quality and accuracy. I haven't been able to find it since.