Saddle

Saddles are items only found in the chests that are inside dungeons; they cannot be crafted. They can be placed on pigs, which allows the player to ride them by right clicking the saddle, but the pig's movements cannot be controlled by the player. Saddles cannot be placed on mobs other than pigs. The player can climb off and on the pig as they please. The saddle cannot be recovered from the pig and will be lost if the pig disappears from the map or is killed. The pig will take any fall damage that may be applicable. It is possible to ride a pig in a Minecart, but only if it has a saddle on.

This video demonstrates a player riding a pig (and being suffocated in a tree).

Trivia

 * By throwing a snowball at the pig while riding it,then throwing again after and repeating, it is possible to ride a pig high into the air.