Crab

Crabs are decapod crustaceans of the infraorder Brachyura, which are generally covered with a thick exoskeleton and come armed with a pair of pincers. In the Crash universe, they also make a few appearances as generic enemies as well.

Crash Bandicoot
Crabs are the first enemies encountered in this game, and, by extension, the entire series. They only appear in the beach section of the level N. Sanity Beach. They do not directly attack Crash. Instead, they simply walk from side to side while blindly snapping their pincers. They are easily defeated with a jump or spin attack.

Crash Bandicoot 2: Cortex Strikes Back
A crab makes a cameo appearance in the first ending, passing by Crash and Coco as she wonders what happened to Doctor Neo Cortex and his Cortex Vortex.

Crash Bandicoot: The Wrath of Cortex
Crabs make a reappearance in the level Crash and Burn, where they randomly scuttle from left to right, shadowboxing at Crash. They can first be found at the beginning of the level when crossing the dock after riding the turtle there. When Crash gets near them, they start punching the air with their pincers.

Crash Twinsanity
Crabs reappear as generic enemies. They appear on N. Sanity Beach and Jungle Bungle where they block Crash by his every movement. Their appearance seems to be a deliberate throwback to the first game in the series. However, these crabs wear shells, implying that they are hermit crabs and, therefore, not the same crabs that Crash fought in Crash Bandicoot. In this game, they can dig underground to pop out of the sand, and ambush Crash.

Crash Landed
Crabs were going to be one of the enemies in Crash Landed before it was cancelled. This enemy only appeared in the DS demo version.

Skylanders: Imaginators
Crabs reappear in Skylanders: Imaginators in the Crash Bandicoot-themed level Thumpin' Wumpa Islands, under the name Bongo Beat Crabs. They are introduced with Hula Chompies.

Their appearance is very similar to how they appeared in the first game, except now they have bongo drums on their back that they beat with their pincers, and they move and attack in time to the music.

Crash Bandicoot N. Sane Trilogy
Crabs reappear in the Crash Bandicoot N. Sane Trilogy, reprising the role they had in the first two games.

Additionally, the crab that appears in the first ending of the second game has a bigger role. While Coco is talking to Crash, the crab walks by them, notices the sleeping Crash, grabs him by the foot, and drags him off-screen.

Personality
As for having three different species, they all have different personalities, some holding no malice and some with the urge to fight.

Crash 1 and 2: These ones have been shown to hold no malice towards visitors or locals, but they are constantly snapping their claws and accidentally harming anything near. As an example, the crab in the regular ending of Cortex Strikes Back simply walks by Crash and Coco without attacking them or running into them. However, the N. Sane Trilogy has the crab in the regular ending drag the sleeping Crash off-screen.

Crash Bandicoot: The Wrath of Cortex: These crabs seem to have the urge to guard their perimeter by shadowboxing from left to right, trying to block out anything coming their way.

Crash Twinsanity: These ones have a much more aggressive personality by ambushing anything that comes by, popping out of the sand to attack it. Crabs in the Jungle seem to try to block creatures out of their perimeter like the previous Crab.

Locations
These crabs have bred in different places, but almost never off of N. Sanity Island. This is demonstrated in Crash Bandicoot: The Wrath of Cortex, where the first Crab off of N. Sanity Island is seen on the volcanic island in Crash and Burn, but of a different species. Hermit crabs have been seen living on N. Sanity Beach in Twinsanity, and oddly enough, in the jungle, but not too far from the beach, making only three appearances there.

Types
The crabs in the Crash Bandicoot series make appearances in several games, but they don't all look or act the same.
 * The original crab is red and walks from side to side. This type appears in Crash Bandicoot and Cortex Strikes Back.
 * In The Wrath of Cortex these ones too walk from left to right, but shadowbox at Crash.
 * In Twinsanity, these crabs walk entirely randomly, even walking over rocks and digging into the sand and popping out in random areas.

Trivia

 * The appearance of crabs as enemies in the Crash games appears to be a reference to the many famous crab enemies from Nintendo's rival Mario series, including Sidesteppers from Mario Bros. and Clawgrip from the true Super Mario Bros. 2.
 * The crab was the very first enemy ever to be introduced in the series.