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.
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.
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 blue 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.
Another variant of the Twinsanity hermit crab was planned but ultimately cut from the game; a "Barrel Hermit Crab". This crab was almost identical to the regular crab except its shell consisted of a metal barrel. This version was originally intended for a zone taking place on Earth where the Evil Twins had drained the ocean for their nefarious needs. One can also be seen on the deck of N. Gin's Battleship in a concept art for the High Seas Hi-Jinks level.
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.
Crabs reappear in the N. Sane Trilogy, reprising the role they had in the first two games. Unlike previously, they have blue eyes instead of white.
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.
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.
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.
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.