Cats are as common in Japan as in the United States, and as frequent in the languages as well. Some expression emphasize perceived positive or negative aspects, while others simply reflect a typical trait, and for the most part there are few parallels in the two languages.
Enter many a Japanese eating or drinking place and you're apt to find a maneki-neko, a "beckoning cat," made of papier-mâché or pottery, seated with one paw raised, inviting customers to enter. It's traditionally considered good luck (for the shop), and is often presented as a gift at openings. Culture-specific words like maneki-neko, which refer to an object or aspect unique to the society, don't translate easily. Another such is nekojita, "car's tongue" the Japanese expression for a person who can't eat or drink very hot foods: we don't generally eat foods so hot that we notice people who can't.
In general, words representing the cat in a positive sense seem to be in the minority in both languages. Beyond the cat's proverbial "nine lives," phrases like "the cat's meow" or "the cat's pajamas," are slangy descriptions of something up-to-date and terrific, though these don't seem to be heard much nowadays. Japanese has karite kita neko "a borrowed cat," to describe someone behaving in an uncharacteristically quiet or well-behaved way, as a cat in unfamiliar territory. And neko kawaigari suru "to indulge a cat" for doting on someone in the way some people care for their cats. We speak of looking like "the cat that swallowed the canary " when a person has an extremely self-satisfied expression. "Curiosity killed the cat," a warning not to be too nosy, seems to be a variant of the traditional "care killed the cat," a warning against overprotection.
For the most part there seems to be a tendency to highlight more negative aspects. Phrases like neko ni koban, (to give gold coins to a cat) "to cast pearls before swine," neko ni katsuobushi (entrusting a cat with a dried bonito) "leaving a fox to guard the henhouse," and neko o kaburu (to put on the cat) "to be a wolf in sheep's clothing," are more common in implying that cats are not so much to be trusted, are sly, or selfish. English "catty," (formerly, "cattish") might used to describe a woman of sly or spiteful character. And something that "looks like something the cat dragged in," is in rather poor condition... like a dead mouse.
Mice of course show up regularly with cats, and so "while the cat's away the mouse will play" warns of behavior without supervision, and "playing cat and mouse," beating around the bush or toying with someone; naku neko wa nezumi o toranu (a meowing cat catches no rats) for big talk with no results. Their relationship with dogs doesn't go unremarked: "fighting like cats and dogs," or "raining cats and dogs" pick up on the traditional animosity.
Many Japanese expressions seem to emphasize the "commonness" of cats. They speak of nekomatagi, "cat-straddling" for a fish that tastes so bad even a cat wouldn't eat it, neko no ko ippiki inai (not even a kitten around) for someplace showing no signs of life at all, and neko mo shakushi mo (cats and ladles too), for "every Tom, Dick and Harry," something as common as could be. When Japanese are so overworked that any helping hand would do, they'd even settle for neko no te mo karitai "to want to borrow a cat's paw." English slang through the years has often used cats as its metaphor, and "cat" has achieved popularity for both men and women. The "hep-cat" of the sixties and earlier was someone who was "with it."
Many Japanese words and phrases merely describe some aspect which is readily noticed, like neko no hitai "(about as small as) a cat's forehead" used frequently to describe a tiny backyard in Japan, or nekoze "a cat's back" for someone with a slight stoop, or rounded shoulders, and nekokke "cat hair" for soft, fine hair on one's head. Similarly neko no me no you ni kawaru (change like a cat's eye) for something that changes rapidly, and the English "cat nap" for catching a quick sleep.
Why we use "let the cat out of the bag," for someone who gives away a surprise or secret before its time, or "what's the matter, cat got your tongue?," when we wonder why someone's so quiet, is unknown. Like the history of the word "cat" itself, the origins of some of these expressions are as mysterious as the Sphinx.