A cage is a small breakable prison that contains innocent creatures that have been captured by hostile characters (eg. Robo-Pirates, Hoodlums, etc). It is Rayman's objective in all three major games, as well as some spin-offs such as Rayman 3 for the Game Boy Advance and Rayman: Hoodlums' Revenge to destroy ever single cage there is and release the prisoners inside them. Cages are possibly the most commonly recurring objects in the Rayman series.
Cages in Rayman
In the original Rayman, the cages are about as big as Rayman is, and they contain Electoons which have been captured by the monsters that appeared after the Great Protoon was stolen by Mister Dark. Each level in the game has six cages which fill up a medallion as Rayman keeps destroying them. When he has freed all six per level, the medallion shows as a happy Electoon face on the world map. There is a total of 102 cages in the whole game, and all of them must be destroyed before advancing to the Candy Château. The game also requires backtracking to find all of the cages, as Rayman is sometimes not able to reach them until he gains his powers. Some cages are also hidden, and only appear if Rayman touches a certain area in a map.
Cages in Rayman 2
Unlike the original game, the player can advance to the final boss level without freeing all 80 cages. The cages in this game are a lot smaller this time, and are mostly hung from ceilings and posts, containing several kinds of creatures and spirits such as Teensies, Familiar Spirits (Rayman Revolution only), Denys, Ludivs (PlayStation version only), and both Yellow and Purple Lums. Also unlike Rayman, they do not appear by touching certain areas in a map, though some are hidden and can only be reached after Rayman receives certain powers, so the player would still have to backtrack. Rayman would know that one is near by hearing the sound of a prisoner crying for help. For every ten that he destroys, his life bar increases, though in Rayman Revolution, it indicates that Rayman has enough Familiar Spirits to unlock another of Ly's minigames (which, when completed, will increase Rayman's maximum health).
Cages in Rayman 3
This time, the only creatures that are trapped inside cages are Teensies that have been captured by the Hoodlums, and there are 60 cages in total. Again, not all of them have to be destroyed in order to advance to the final boss level, but backtracking will still be needed for maximum health. Reminiscing the original Rayman, each cage that is destroyed fills up a medallion, though this time when each medallion is filled with 6 cages, Rayman's life bar increases. The cages in this game look different to the other games, as they are wooden in the structure of a bird-cage, tied to a balloon that suspends it into the air. According to the official description, the Teensies shut themselves up in the cages so the Hoodlums wouldn't have to build them in vain.
Cages are also found in all Rayman games on the Game Boy Color and Game Boy Advance.