From the Super Mario Wiki
Chomps are, essentially, chainless Chain Chomps. They are much bigger than normal Chain Chomps, setting the standard for their huge sizes. Also, chomps seem to have more humanlike teeth than regular chain chomps, although in their first appearances they had triangular teeth.
Super Mario World 2: Yoshi's Island / Yoshi's Island: Super Mario Advance 3
Chomps debut in Super Mario World 2: Yoshi's Island. They jump from the background hills and destroy everything that is below them. They seem to be unlimited in number on the background hill or they come back to the same hill after jumping. They appear only in certain levels, when a sign with one of them on it appears. Yoshi doesn't lose Baby Mario when hit by one of these enormous monsters. Chomp Rocks, which are stones in the shape of Chomps, also appear. Another type of gigantic Chomps called Chomp Sharks also appear.
Chomps reappear in Yoshi's Story, where they act almost identical as they did in Super Mario World 2: Yoshi's Island. They only appear on Jungle Hut, World 4-1, where the Baby Yoshis must avoid these enemies to get past. This is also the first game in which they are explicitly named Chomps.
Yoshi's Island DS
Yoshi's Island DS introduces another new sub-species, Stompin' Chomps, which main method of attacking is bouncing around the stage, trying to squash Yoshi. They usually appear in groups, and are smaller than regular Chomps.
Chomps, Shark Chomps, and Stompin' Chomps only appear in the level Rompin' Stompin' Chomps.
Chomp Rocks also reappear. In the level Return of the Moving Chomp Rock!, one is required for crossing deadly spikes and other dangers.
Mario & Luigi: Partners in Time
In Mario & Luigi: Partners in Time, just as the four heroes are heading through the Warp Pipe to get to the top of the Princess Shroob statue in Shroob Castle, a Chomp leaps out of the basement's sewer water and bashes the pipe, redirecting it's destination to the basement.
Later, as the brothers are about to hit an Exclamation Mark Block to cross a pit of spikes and leave the basement, the Chomp leaps out of the water, eats the block, and heads into one of the five Warp Pipes visible on the map. The player must use the Star blocks that appear to damage the Chomp four times. However, on the final attempt, Chomps fill up all the pipes. The player can tell the correct Chomp apart from the others by looking at which one is barking the fastest. When it is defeated, the Chomp is destroyed and the block heads back to its original position.
Super Mario series
Super Mario Galaxy
Chomps appear in Super Mario Galaxy and roll straight off the planetoid, without trying to hurt Mario or Luigi in a similar way as Piranhabons from Super Mario Sunshine. If Mario or Luigi is to step in front of the Chomp, he will be knocked over and hurt. In the Single Player Mode, Chomps can only be defeated with the use of a Rainbow Star, a Stretch Plant, or a Bob-omb. In the Cooperation mode, one player can hold one Chomp's back still while the other player spins it in the front, or one player makes one Chomp stunned while the other collides with it, which will make them explode into many Star Bits.
Super Mario Galaxy 2
In Super Mario Galaxy 2, Chomps reappear, first in the Flip-Swap Galaxy as the common obstacle there. They later reappear in the Chompworks Galaxy, where they make their most prominent appearance, the galaxy being focused on them. Chomps behave the same way as they did in Super Mario Galaxy.
Mario Kart series
Mario Kart 64
Mario Kart Wii
A Chomp also appears as a stage hazard in Chain Chomp Wheel in Mario Kart Wii. After being shot out of a cannon at the beginning of the battle, it rolls around in the mid section of the roulette wheel, and squishes any racers who it runs into it. It looks exactly the same as the Chomps in Super Mario Galaxy. They also appeared in the 2nd November 2009 tournament.
Mario Kart 7
Chomps also appear on Mario Kart 7's Rainbow Road. They appear on the moon portion of the track, rolling around the area. Players who run into a Chomp are knocked back and, like with every other hazard in the game, lose three coins.
Mario Kart 8
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