Sometimes Rayman's shoes have some significance to the plot despite simply being body parts.
At the end, Rayman is thought to be dead after Razorbeard's ship blew up with him inside. At his funeral, his shoe is placed on top of Polokus's pedestal. Rayman then reappears with only one foot. It is possible that either Rayman was barefoot in this game, or he got new shoes for Rayman 3.
In the British Rayman M version of Rayman Arena, the intro video shows Rayman without his shoes, revealing his socks- yellow, with blue polka dots.
Rayman's shoes change in appearance drastically in this game. At the beginning of the game, before Rayman gets his fists back from Globox, they are replaced with his feet. Rayman can kick by using the regular punching button. There are points in this game where Rayman's left shoe flies off, Rayman shrinks to the size of it, and lands in the right one. This begins a little mini-game where Rayman drives his right shoe, and has to blast into his left one. The only thing the shoe can do is scoot away from you. Your shoe actually has a turbo power which you can use to go much faster for a certain period of time. To gain control of your left shoe again, ram into it about three or four times, and everything will be back to normal. Completing this mini-game usually rewards Rayman with a laser detergent can which allows him to proceed to the next area.
Rayman throws his shoe at the TV in an attempt to destroy it, and succeeds.