My late grandfather had a grey moggy he taught to do a trick. Originally food was the reward but in the end it wasn't necessary.
He used to stand right behind her, and link his hands in front to form a closed loop. The cat would leap up and jump through the loop.
She liked doing the trick without any reward because she used to wind around his legs and then stop and look up expectantly. Not surprising I guess because cats like jumping up...but it was also because they were great mates.
