Plums are large bouncy fruits that are found commonly throughout the Rayman series. They are usually purple in colour, and grow at a very fast rate. A plum can be knocked down from its plant and used as a platform or as a tool to despatch enemies. Plums, along with cages, are some of the very few items that have appeared in the original Rayman, Rayman 2 and Rayman 3 (though they are absent from Rayman Origins and Rayman Legends). In Rayman Junior, plums are referred to as Bongo Berries.
In Rayman and its spin-offs
In the original Rayman game, plums are used primarily to float through water. They can also be made to drop onto the heads of Livingstones, making them less dangerous: it then becomes possible to jump onto their plum-encased heads and use them as walking platforms, but directly touching the Livingstones will still cause damage. When the plum is on the ground (where it keeps bouncing), Rayman must hit it with his fist to move it, whether he's in front of it or on it (in this case, he'll have to shoot and then duck to ensure that his fist hits the plum when returning to him). Once in water, it floats in whichever direction Rayman is looking in, allowing him to control it with ease.
Plums can also be seen attached to vines, these plums will swing in a parabolic shape when punched, and can be used to convey Rayman forward in levels, provided he times his jumps right in order to land on the plum, and depart from it.
In the Atari Jaguar, PC and mobile-exclusive Breakout minigame, Rayman must use a ball to make a cluster of floating plums of various colours vanish. Some of these plums have special properties, such as being very bouncy. Some cause the entire plum cluster to move when they are struck. Occasionally plums in this minigame begin to flash with multiple colours; hitting a flashing plum will cause it to vanish and also release a collectible item such as a Ting (or others, depending on the version).
A plum stuck on the head of a Livingstone.
Plums return in Rayman Designer and its spin-offs where there are three different versions which have different bounce speeds. Swinging plums also make a return.
In Rayman 2
These strange fruit have several purposes. You can throw them at your enemies, climb onto them and move around by shooting in the opposite direction, and even float through lava fields on them...—Manual, Rayman 2
These huge plums fall to the ground from their trees, or can be unhooked by shooting. They have multiple uses: as a weapon, by throwing them on the head of enemies, or as a conveyance. In the latter case, once a plum is on the ground, climb on it, and to steer, shoot in the opposite direction to that which you wish to take. Note that the plum has resisted even lava.—Official description, Rayman 2: The Great Escape : Le Guide Officiel
In Rayman 2, plums are used to travel over rivers of water and lava. They can also be thrown at Gorilla Pirates, who will be rendered harmless and can be used as makeshift platforms due to the plum being stuck on their head. Rayman can move plums by shooting at them if they're in front of him, or by shooting anywhere if he's on it, which will move it in the opposite direction. Plums bounce endlessly, even on lava, however they can be destroyed if they fall into pits of hotter, yellow lava. It is also possible to throw them onto posts, permanently or temporarily (in this case, the goal is to take the plum to a precise place), allowing Rayman to reach places he otherwise could not. Oddly enough only plums from specific plum trees will stay on the posts. For the posts where the plum will fall off after a few seconds, it's not actually the post itself which is unstable, but rather that specific type of plum.  
Plums also appear in the Game Boy Color version of Rayman 2, in which they are only used to travel through bodies of lava. They are mostly purple, but, notably, they can also be green in this game.
In Rayman M
Plums do not make an appearance in Rayman M, however it is believed to exist a different kind of plum with a conical form and eyes in the top of the leaves. It is unknown if this kind of fruit is intended to be a plum variant or not.
In Rayman 3
Beware! The Plum is an extremely hallucinogenic fruit. Don't pass one by without having a nibble.—In-game description, Rayman 3
In Rayman 3, plums are much less bouncy than in the other games, and are no longer buoyant. Their sole purpose is to be picked up and thrown onto posts, thus creating platforms which can be used to reach high places. On these plum-posts are pictures of Livingstones; an in-joke referring to the Livingstones' susceptibility to having plums lodged on their heads in the original game. As was the case in Rayman 2, Rayman can carry them around with him; they have their own musical theme which plays in the background until they are thrown successfully (or at one point, unsuccessfully) onto a post. If Rayman is close enough to a plum, he can also kick it, sending it flying through the air.
Early on in the development of Rayman 3, carnivorous plants named Hoovers were planned to appear. These plants loved to devour plums, and Rayman would have had to feed them in order to pass. However, they were cut from the final version of the game and replaced with the more straightforward plum-posts.
Plums also make an appearance in the Game Boy Advance version of Rayman 3. They are found only in one level, River of Fire, where their only purpose is for Rayman to jump on them and sail them across the lava to progress through the level. They cannot be picked up in this game.
A plum, as seen in the Game Boy Advance version of Rayman 3.
Plums reappear in the Game Boy Advance version of Rayman Raving Rabbids, where they can be used in a number of ways. They are much larger here; they do not bounce any more, and Rayman can carry them again. He can either throw them against spiky walls or spiky ground to create platforms, or in the water to sail through the swamps, though he can no longer control their direction. Thrown plums can also break cages and kill enemies, as can walking into enemies while holding a plum.
Rayman sailing on a plum.