A crab was a type of crustacean found on several planets, including Earth.
When Spock tried to match the sound of the Whale Probe to the sound of various Earth animals while using the phylum search mode aboard the Klingon Bird-of-Prey HMS Bounty in 2286. Among the search results was the name and image of the crab species Cancer productus, along with a second image of a crab paired with the species name Vulpes velox. (Star Trek IV: The Voyage Home)
Crabs were Ferengi delicacies. Grand Nagus Zek's son Krax was fond of crabs. (DS9: "The Nagus")
Keiko O'Brien often made crab rolls. (DS9: "Tacking Into the Wind")
A species of burrowing crab was present on the planet where the shuttlecraft Yosemite crashed in 2381. A group of them attempted to carry off AGIMUS, but they were driven away by Ensign Brad Boimler. (LD: "Where Pleasant Fountains Lie")
Cooked crabs on ice were available at Sisko's Creole Kitchen in 2381. (LD: "Grounded")
In the original script for "The Cage", Talos IV was named Sirius IV and was inhabited by crab-like aliens who kidnap Christopher Pike.
In deleted scenes from Star Trek, the Klingons captured the Narada after the USS Kelvin crashed into it, and imprisoned Nero for the next twenty-five years. These Klingon guards wore helmets and thick coats, which costume designer Michael Kaplan respectively modeled on a horseshoe crab and elephant and rhino skin. (Star Trek - The Art of the Film, p. 42)