Tarantulas are a class of large and hairy arachnids, itself part of the Theraphosidae family of Earth spiders. Some of the larger tarantula species are among the largest spiders of Earth.
Three million years later, at least one tarantula was known to have survived aboard the spaceship Red Dwarf. Although tarantula are largely harmless to humans despite their size, and their venom not fatal, at least two of the boys from the Dwarf - Rimmer and Lister - have phobias of tarantulas.
When Rimmer's Better Than Life fantasy began to fall apart because of his multiple neuroses, he imagined a tarantula crawling up his trousers. This immediately came into existence, and Cat pointed out that a huge, black, furry spider with big teeth just crawled up his trouser leg. Rimmer was terrified as it was the thing of which he was most afraid. Lister told him to wish it away, but instead a terrifying Tax Man appeared instead, threatening violence. When Rimmer tried to wish the Tax Man away, they all ended up buried alive on the beach instead. ("Better Than Life", Series II).
Lister also shared this fear of tarantulas. When Kryten's "hand spider" arrived on Red Dwarf to get help from Lister, Holly warned Lister that he had detected something very like a tarantula coming out of an ore sample pod was loose aboard the ship. He was very nervous, since the thought of a tarantula crawling over his sleeping, helpless body was a particular phobia. When the hand spider crawled up his leg, he used a keyboard to write out a warning to Cat. He typed that a "Taranshula" was in his boxer shorts and was trying to make a nest. When the Cat saw it, he also began to type instead of talk, writing that the spider had an eye the size of a meatball. Lister asked Cat to kill it, but the hand crawled up onto the terminal and typed out "Hello. Kryten in danger. No time to explain. Follow." Lister was relieved and Lister and Cat took a Starbug down to the Psi-moon to help Kryten. ("Terrorform", Series V)
When Lister was later taken hostage by the Lows on the Low Red Dwarf, they took control of his body with the Spinal Implant and tortured him for fun. One of those tortures was to eat a tarantula which they had in a small tank. Lister was made to kneel down and open the tank, pick up the spider, hold open his mouth with one hand and shove the tarantula in with the other. After swallowing the spider, he declared the Lows to be "two lettuces short of an allotment" ("Demons & Angels", Series V).