From the Super Mario Wiki
Whomps are enemies who somewhat commonly appear in the Mario series. They are large, stone enemies that resemble stone rectangles with faces, hands and arms and feet (without legs). They are the minions of Bowser and the Whomp King. They debuted in the game Super Mario 64. Whomps are related to Thwomps, enemies that are also made out of stone.
Super Mario series
Super Mario 64
Whomps first appear in Super Mario 64 as rare enemies. In this game, they attempt to crush Mario by falling over and trying to land on top of him when he gets near. They can be defeated by Mario causing them to fall over and subsequently ground pounding on their bandaged backs, their sole weak spot. Mario can also jump just as the Whomp is about to fall on Mario to pass through it and get on its back. Whomps appear mainly in Whomp's Fortress, the residence of the Whomp King, a giant Whomp who rules over the Whomps and Thwomps, as well as the stage Bowser in the Sky. When a Whomp is defeated, Mario will be rewarded with three coins.
Super Mario 64 DS
Whomps reappear in the Super Mario 64 remake, serving the same purpose as in its predecessor. They have been modified to look more like they do in recent games. Additionally, it is no longer possible to jump through them as they fall.
New Super Mario Bros.
Whomps reappear in the Nintendo DS game New Super Mario Bros.. They are exclusively found in the castle of World 3. In this game, Whomps look slightly different as their once purple hands are now the same color as their body. Whomps in this game behave similarly to their Super Mario 64 counterpart, again trying to crush Mario if he attempts to pass by them. Once on the floor, Mario can Ground Pound the Whomp's back to destroy it. They can also be used as platforms to cross harmful parts of the environment, like Spikes. One particular Whomp can even be used to help Mario collect a Star Coin. There is also one particular Whomp, known as the Big Whomp, who behaves differently from the others, being slightly larger and walking instead of staying in the background. However, the official strategy guide doesn't make any distinction between this particular Whomp and its brethren. Due to where this Big Whomp is placed, it can not actually move and simply appears to aimlessly turn back and forth on the spot. This is likely due to bugs that would have occurred, as beta screenshots show a Big Whomp chasing Mario and Luigi.
Super Mario Galaxy 2
Despite not appearing in the prequel, Whomps appear in Super Mario Galaxy 2, with many of their physical features changed. The Whomps' body features are more rectangular. Their characteristic bandages are no longer present; instead, Whomps now bear the Ground Pound symbol on their back. Additionally, they can cause Mario to lose all of his health points in this game, unlike in their past appearances. To defeat them, Mario needs to ground pound on their backs when they are on the ground. The area in which to Ground Pound them is now limited to the small Ground Pound symbol on their back, instead of the whole back. Mario can also do a Wall Jump on them, which is necessary to get a Comet Medal in Bowser's Lava Lair.
New Super Mario Bros. 2
Whomps once again appear in the Nintendo 3DS game New Super Mario Bros. 2, alongside Big Whomps. They act just like they did in the first New Super Mario Bros. game. Regular Whomps are now seen walking back and forth sometimes, and some Big Whomps are seen in the background. Regular Whomps only leave behind one coin when defeated in this game, while Big Whomps leave three. They are only found in World Mushroom- and World Star-3.
Mario Party series
In Mario Party, 4 Whomps appear in DK's Jungle Adventure. They are guarding the junctions, and players who wish to take the path that a Whomp is blocking must first pay it 10 Coins. Players that choose to take the path that the Whomp is not guarding causes the Whomp to start blocking that pathway instead.
Mario Party 2
In Mario Party 2, Whomps appear in Horror Land and Space Land. In Horror Land, they keep their role of Mario Party, but overnight they are paralysed by magic and can't move, this forces players to take the open way. In Space Land, they pursue players instead of Thwomps if Snufit Patrol is out. Whomps also are in the minigame Day at the Races. Also, a Whomp with no legs and arms appears in Mystery Land.
Mario Party 3
Whomps appear in Mario Party 3, in the Duel Mode, as Donkey Kong's initial partner. They have four health, but no attack power. Their salary is 3 coins per turn. If the player receives a second Whomp as a partner while one is still active, the Millennium Star decreases their salaries by one instead of raising their attack.
They also appear on the board Creepy Cavern. On this board, the primary Whomp is the Whomp King, who is blocking one of the two paths at an intersection; giving him an item allows the player to move on while the Whomp King blocks the other path. There are also three Whomps right next to him, who appear to be playing an actual Mario Party board game, which appears to be Rules Land from Mario Party 2.
Mario Party 4
In Mario Party 4, a Whomp hosts the Extra Room, a room filled with challenging minigames.
Mario Party 5
In Mario Party 5, Whomps and other characters appear in the background of Random Ride. They also appear in the background of many other minigames. On the Pirate Dream board, they give players a lift to the top of the hill for 10 coins.
Mario Party 6
In Mario Party 6, a Whomp blocks a path in front of an Orb Shop in the board Snowflake Lake, and charges 10 coins for players to pass. Going this way will take the player to the right side of the frozen pond.
Mario Party Advance
One Whomp also appears as a character in Shroom City, guarding the first floor of the Duel Tower. This Whomp challenges the player to the game Stair Scare. If the player wins, he says that he will leave to train. The ending of the game says that he became friends with Thwomp. At one point, he came over and somehow got into his house.
Mario Party 7
In Mario Party 7, now with their gray hands, they appear in a few minigames such as Sphere Factor and Spin Off. In the latter they are one of the possible pictures to be formed, and in the former they are obstructions.
Mario Party 8
Mario Party DS
Mario Party 9
A Whomp appears as one of the bosses in Mario Party 9, alongside Big Bob-omb as the boss of the board Bob-omb Factory.  It is the mid boss of the level, and the minigame it is fought in is Whomp Stomp.
Mario Party: Island Tour
In Mario Party: Island Tour, a Whomp appears at the end of the Perilous Palace Path board, acting as the final challenge. The player rolls a die to try to deplete its health. However, if the player does not fully deplete his health, it will squish them and the player will not be able to finish.
Mario Golf: Toadstool Tour
Whomps re-appear in Mario Golf: Toadstool Tour, but their roles are quite minor. They appear in the Bowser Badlands squishing the player's golf ball, and therefore the player has to take a penalty stroke.
Paper Mario: Sticker Star
Whomps make their Paper Mario debut in Paper Mario: Sticker Star. Originally, Whomps were going to appear as regular enemies, but in the final product only one Whomp appears, during the second phase of the final battle with Bowser. During this portion of the battle, the Whomp defends Bowser from any attacks (including those that hit multiple enemies). It attacks by walking up to Mario and either swinging its arms at him or slamming down on top of him; whenever Bowser attacks it moves aside, briefly exposing then covering the scissors image on its back. The Whomp only takes one HP of damage for every attack, but is toppled whenever an Eekhammer is used on it, allowing it to be temporarily damaged normally (using any other kind of hammer causes it to stumble, but recover).
Whomps are somewhat similar to Thwomps, but they resemble stone slabs instead of cinder blocks. They have arms and legs, and in their debut, Super Mario 64, they wore purple gloves, and their hands were ball-shaped. In its remake and later games, their hands are bare and mitten-like. Like Thwomps, they have sunken-looking glowing red eyes.
Their faces seem to be distorted or disfigured, possibly due to their lone attack of slamming to the ground, and their faces seem to be more deeply carved and also more three-dimensional, as opposed to the Thwomps' flat faces. In most titles, Whomps have adhesive bandages in an "X" shape on their backs, but in Super Mario Galaxy 2, they have a carved circle with the Ground Pound symbol on it.
Names in other languages