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, terrifying Rimmer as it was the thing of which he was most afraid. Lister told him to wish it away, but they all ended up buried alive on the beach instead (RD: Better Than Life).
Lister also shared this fear. When Kryten's hand arrived on Red Dwarf to get help from Lister, Holly warned Lister that something very like a tarantula was loose aboard the ship. He was very nervous, since the thought of a tarantula crawling over his sleeping body was a particular phobia. When the hand crawled up his leg, he used a keyboard to write out a warning to The 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 wanted to kill it and was very relieved to discover it was Kryten's hand (RD: Terrorform).
When Lister was later taken hostage by the Lows, they took control of his body 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" (RD: Demons & Angels).