Crab

Crabs are a species of animals found in a few Mario games. They are often portrayed in either the same way as their Real World counterparts or as enemies.

Mario Bros.
In the original Mario Bros. arcade game, there is a crab-like enemy known as Sidesteppers, which looks similar but acts differently to crabs. Also, the manual for Super Mario Advance labeled Sidesteppers as Crabs.

Super Mario Sunshine
Small crabs populate the beaches of Super Mario Sunshine. They have no affect on the gameplay and are simply used for decoration.

Super Mario Galaxy
In Super Mario Galaxy., there are red and blue Crabs found in many beach galaxies. To defeat them, Mario must jump on it or Spin them to put them on their guard which will cause them to retract into their shell, allowing Mario to circle behind them and Spin their weak point to defeat it. There are also Blue Crabs, however they are more skittish and when they are defeated they leave a 1-up Mushroom. The red and blue coloring seems to be a direct reference to Sidesteppers.

Mario Kart series
In the Mario Kart series, Crabs can be found mostly on beach stages where they walk left and right. Driving over one will make the player spin around. Sidesteppers have replaced crabs in later installments.

Donkey Kong (Game Boy)
Crabs also appear in Donkey Kong on the Game Boy. They make their first appearance in stage 1-2 on the Ship. Crabs walk around slowly, and sometimes stop and hide in their shell. Mario can stand on them fine, but if he walks into them from the side, he gets killed. Crabs also try to kill Mario by reaching out to him with their extensible claws.

Donkey Kong Country
In the Donkey Kong Country remakes for Game Boy Color and Game Boy Advance Donkey and Diddy Kong may encounter a Crab during a challenge at Funky's Fishing. The Crab has no affect on the Kong's' score, but if they can succeed in hooking it, they will earn themselves a special Photograph from Funky Kong. It scurries across the the bottom of the water rather quickly, and appears randomly, so the Kongs should always keep an eye out for it. Once the Crab is caught, it will never reappear.

Trivia

 * In Super Mario Sunshine one of the Islands neighboring Isle Delfino is shaped like a crab. It is seen in the opening cinematic.
 * Sidesteppers and crabs all go by the generic name "crab" in other countries (including Japan), strengthening the theory that they are all meant to be the same species.