Cat
The Felidae family, general known as cats, are a group of carnivorous mammals that has species native to all continents except Antarctica. Indeed, they are only family within the Carnivora order where all members are carnivorous. Cats include several of the most dangerous and iconic predator animals including the lion, tiger, bobcat, leopard, cheetah and puma.
While humans have domesticated the cat's arch-rival, the dog, for over 10,000 years, cats have only been domesticated for a few thousand. Even using wild felines as execution method is only known to go back to the time of Alexander the Great (c. before 300 BCE). While dogs have been used to fill a variety of tasks, domestic cats are primarily used for pest control, since they kill rodents and other threats to stored food without taking much interest in the supplies themselves. Since cats tend to eat these pests, they are fairly self-sufficient guards.
Cats have the ability to break spacetime occasionally by expanding to fill all available space, an ability accurately depicted in Dwarf Fortress.
Dungeons and Dragons
Domestic cats have long been an option for a Dungeons and Dragons familiar. Larger cats are typically favored forms of Druids who transform into animals or take animal companions. This is especially so in 3E, as they tend to have Pounce, which dramatically increases their attack power by letting them full attack and move on the same turn.
The Killer Housecat
In 3rd Edition Dungeons and Dragons, house cats have stats that make them incredibly deadly combatants for their apparent harmlessness and low Challenge Rating. Thanks to a tiny size and high dexterity, a cat has an armor class that makes it as hard to hit as a man in a chain shirt. The cat is actually harder to hit, since that AC is all touch AC, so splash weapons and energy rays will not save you. They are also very stealthy and win initiative, so they can ambush easily.
A cat has three natural attacks, all doing 1 damage each; statistically, a cat will virtually always kill a level one Commoner one on one, and possibly even a level one Wizard if there's no familiar helping them fight back. Even if he can get casting off (which is already a resource expenditure far in excess of its supposed CR), the few first level Wizard spells available aren't that likely to work on the monster thanks to low damage that is likely halved (and if it's a familiar attacking you, outright avoided) by the cat's high reflex save. More meaty classes fare better, but still need disproportionate effort to kill it.
Pathfinder nerfs them slightly, but only through a minor, easily overlooked system wide change: Damage reduced to less than one by damage penalties does one non-lethal damage (in 3E this was still lethal damage). This means a victim has a chance of being rescued after being KOed, but before the cat finishes them off. This does raise the question of how cats can actually kill rats without first KOing them; then again, that's not unrealistic to RL cats, who usually try to cripple their prey before going in for the killstroke (because the killstroke generally leaves the cat vulnerable, so making sure their prey can't fight back is important).
The "killer housecat" phenomenom is well known enough that it's referenced regularly in 3e forums and its derivatives as a standard deadly "monster" for its CR and to emphasies how squishy low level Wizards are, as well as other games and media in or neat the /tg/-sphere.
Cats in Magic the Gathering
The cat is one of the oldest creature types in the game. It first debuted in Alpha, though the first one to be printed with the type on it was in Legends. While most creatures with the Cat type are anthropomorphic of some kind, be it Catfolk, Rakshasa or Ajani Goldmane, there's plenty of actual predators represented. "Normal" cats tend to be green, since it is (naturally) the color of wild beasts. Some cats are white, since they're a symbol of many white values like the group and knightly virtue. Oketra of Amonkhet is a psuedo-Eygptian deity that considers cats sacred. Cat tribal is quite rare.
Whitemane Lion is a notable cat card that has been printed several times. It has an effect that requires you to return a creature to your hand when you summon it. This effect seems like a drawback, but is actually key to powered many decks that abuse it to repeatedly trigger enter the battlefield effects. One of these combos is with, fittingly enough, Oketra's Monument. These two allow you to spawn as many 1/1 tokens as you have white mana for.
Not to be outdone by the other Wizards of the Coast game, Magic also contains a lethal house cat. Sanctuary Cat debuted in Innistrad. It normally wouldn't be a notable card; it's a 1/2 white one drop and a functional reprint of one of the oldest cards in the game with a generally worse type, and a few strictly better cards have been printed. This card became notable because the art depicts what seems to be a normal cat, and since 1/1 has always been the normal power and toughness for one-mana creatures, this cat can kill a surprising number of things and live. Most of these creatures are still trained and armed/armored soldiers.
Cats in Warhammer Fantasy
Like in old folklore stories, Queen Neferata, the first Vampire and head of the Lahmian Bloodline, likes to turn her underlings (usually female) into cats to sneak into the homes of men (or women) of high standing. The shapeshifting ends, and the Vampire seduces their target leading to them either being their mysterious mistress (in all applications of the word) or their mysterious relative/spouse nobody had heard of. Either way, Neferata gains another pawn in her plan for world domination. In old Lahmian models cats often appeared alongside the Vampire.
Cats in Warhammer 40k
It was confirmed in one of the Ciaphas Cain books that humans still keep cats as pets. And when you consider how many rats and shit must be in those hive cities, it's not exactly surprising. They would be quite at home on a ship of the Imperial Navy, but sadly, many might also just be food for hive world inhabitants and feral worlds, anywhere where food is hard to find (much of the Imperium).
IRL relevance
The main point of IRL overlap between cats and /tg/ (besides the panoply of cat-themed board games) is that a cat will knock over all the fiddly bits of your game if you let them. Preventing this is difficult, particularly if the pieces are of the right size to make a cat think "hey, this looks like it might be edible". While cats are usually smart enough to not eat inanimate objects (unlike dogs), a cat will attack unusual small objects like game pieces in order to make sure it's not just a small animal that's playing dead.
Cats in mythology
Domestic Cats played a large part in Egyptian religion. They were the most frequently mummified creatures. We don't know why they did this or their exact purpose, though we do know Egyptians were among the first to domesticate the cat.
Japanese myth has the nekomata. These two tailed cats vary between large, man-eating monsters and magically-inclined though generally-peaceful variations of domestic cats.
Black cats allegedly bring bad luck. They are a favored familiar of witches.