My old cat Charlie would sulk by turning his back.
On one occasion my friend picked him up so he was facing me, Charlie turned his face away, my friend moved his head and he actually moved his eyes so as not to look at me. Of course by this time me and my friend were in stiches which didn't go down well.
Another time there were a group of us and somehow we had offended him, so he found the only spot in the room where he could have his back to us all. It took him a good 5 mins.