The film consists of three stories linked together by a cat as he wanders from city to city, seeking out a little girl (Drew Barrymore) in order to save her from a supernatural danger. As a result of it's wanderings, the cat plays a minor role in the first two stories and a significant part in the third.
In the first tale, set in and around New York City, the cat is captured by a man who works for a self-help firm called Quitters Inc, that aids people in quitting smoking. On a busy NY street, a man, Dick, is driven to an office building by a friend who tells him "These guys'll change your life." At his first visit, his counselor, Vinnie Donatti, asks Dick for all his cigarettes and crushes them wildly on his desk. Dick tells him that this form of treatment leaves much to be desired, however, Donatti gets to the actual treatment. He opens a large set of curtains in the room, showing a white room containing a cat eating at a small bowl. Donatti flips a switch that sends a low charge of electricity into the floor of the room, causing the cat to jump around wildly. Donatti cuts the power after a few seconds and explains to Dick that the association of pain with eating may one day cause the cat to starve in front of it's dish. Donatti tells Dick that his treatment begins right away; there will be people watching him constantly, night and day. If Dick smokes one cigarette, he will be punished. Dick suggests that they will bring him in and give him the shock treatment. Donatti says it will not be Dick, but his wife that will be tortured in the room. Further treatments will be increased voltage and beatings of both him and his wife. If he's unable to give up smoking after 30 days, he will be killed.
Dick goes home very troubled. Late at night, he sneaks into his home office and begins to light a cigarette when he hears a noise from the room's closet. Though he's not completely certain anyone is hiding in the closet, he still tells the person that he didn't actually light the cigarette. Dick is able to keep from smoking for several more days until he's stuck in traffic. He opens his glove compartment looking for some gum and finds an old pack of cigarettes. He ducks below the dashboard and lights up, waving the smoke off. When he looks over to his left, he sees one of Donatti's men drive off, smiling evilly. Dick races home and finds his wife gone. He gets a phone call from Donatti, who tells him to report to Quitters Inc. When he arrives, he sees his wife in the cat's room. He tries to free her by breaking the glass and Donatti's goon subdues him and makes him watch his wife being shocked. Dick is devastated and wonders how he'll explain everything to his wife. Donatti says he may be surprised at how his wife takes the news. His wife seems to understand that Dick has done this for her and for his mentally-impaired daughter, who lives at a special boarding school.
Several months later, Dick receives another phone call from Donatti. Dick has been cigarette-free for that long but Donatti says they need to discuss another issue. Dick has gained a significant amount of weight, something that happens to the majority of Donatti's clients. He prescribes some illegal diet pills for Dick and tells him to use them wisely. If he's unable to control his weight, Donatti will send someone to Dick's house to cut off his wife's little finger. Some time after that last meeting, with Dick successful at keeping his weight down, he and his wife have dinner with the man who originally told Dick about Quitters Inc. The group makes a toast to Quitters Inc. Dick's friend's wife, however, is missing her little finger.
The second story opens in Atlantic City with a rich businessman, Cressner, betting on the same cat (which had escaped from Quitters Inc), seeing if it can cross a busy street safely. Though it causes a minor car crash, the cat makes it safely and Cressner decides to keep it for a pet.
In another part of the city, a man, Johnny Norris, a tennis instructor, is beaten and kidnapped by two of Cressner's thugs. He's brought to Cressner's penthouse where Cressner tells him that he knows he's been having an affair with Cressner's wife. Cressner offers Norris several options: he can agree to indentured servitude to Cressner for several years and be free, but not see Cressner's wife again, or he can skirt the entire outside of the building on a ledge about five inches wide, about 300 feet above the ground. If he completes the entire circuit, he'll be free and he can have Cressner's wife. If Norris refuses both options, the police will be tipped off about a kilo of pure heroin Cressner's thugs have hidden in the trunk of Norris' car.
Norris agrees to walk the ledge outside the building. Completing the entire circuit around the building takes him about three hours. Along the way, he encounters sheer winds at the corners and is constantly taunted by Cressner himself, who sneaks into the penthouse opposite his own and honks a horn in Norris' ear through an open window. After Norris battles a pigeon that pecks his ankle, nearly sending him plummeting to the street, he stops in the window well of another penthouse. When Cressner discovers him there, he uses a fire house to soak him and threatens to blast him over the side.
Before Norris makes it back to the outdoor balcony of Cressner's penthouse, Cressner has his goon, Tony, bring in a bag of money and a small Styrofoam crate, telling Tony to "put it on top of the money" in the bag. When Norris finally makes it to Cressner's balcony, he climbs over the railing and is immediately grabbed by Tony, who takes him at gunpoint to his boss. Cressner says he'll honor the bargain and give Norris the money and his wife, however, when he kicks the bag, a severed head flies out... it is his wife's head. Cressner orders Tony to shoot Norris; as Tony takes aim, Cressner's cat trips him up and he loses his gun (the cat runs out the apartment's open door to freedom). Norris seizes it and shoots Tony, then holds Cressner hostage. Cressner pleads for his life, offering several million dollars. Norris refuses and makes a simple wager... the next scene shows Cressner on the same ledge he forced Norris to skirt. Cressner gets moving, making it around the first corner. However, when he reaches the side of the building where the pigeons roost, one begins pecking his ankle. Cressner kicks a bit too hard at the bird, loses his balance and falls to the street. On the ground, the cat silently witnesses his impact.
The cat makes his way to a suburban town on a delivery truck in Wilmington, North Carolina. There, he is taken in by a young girl, Amanda (the same girl from the vision in the opening scene), who names him "General." Amanda's mother immediately disapproves of her keeping the cat as a pet, saying that "cats can steal a young girl's breath" while they sleep. That night, the cat sleeps in Amanda's room. While the child sleeps, a hole opens up in a baseboard and a small, ugly troll emerges. He tries to climb up on Amanda's bed, but is startled by the cat and a short battle ensues, resulting in the troll's escape back into the hole it opened, which is immediately closed up. Amanda's parents, having heard the ruckus, burst into her room. Her mother immediately blames the cat for all the damage and assumes the cat was attacking her daughter. Amanda defends General, telling them about the troll. Naturally, they don't believe her, thinking she had a nightmare.
The next day, while Amanda is at school, her mother lures General into a pet carrier and takes him to the pound, which leaves Amanda very upset after she gets home. At the pound, General is to be euthanized; Amanda's mother had told the staff there that the cat had attacked her daughter. One of the staff opens his cage and the cat escapes, running back to Amanda's house.
In the girl's bedroom, the troll again emerges from the baseboard and places a small wedge under the door to keep intruders out. He crawls up to Amanda's bed, where she's fast asleep. He begins to use a form of magic that draws Amanda's breath from her mouth. Amanda quickly becomes distressed, finding it difficult to breath in her sleep. After a few moments, General finds his way in through the chimney shaft and immediately attacks the troll. They battle again throughout the room until the cat corners the troll on Amanda's small record player. General hits the button that starts the record, spinning the monster around. General then hits the switch that changes the rotation to 78 rpm; the troll is unable to hold on very long and is flung across the room into a fan, where it's mutilated, leaving behind a few recognizable body parts. Amanda's parents, who had been pounding on the door but unable to enter because of the doorstop wedged there, finally burst in. The mother is furious at seeing Amanda holding the cat, however, Amanda is able to defend General this time, pointing them toward the wrecked fan and the troll's remains. Her father sees one of the monster's arms, as well as it's tiny sword. They look at the weapon, bewildered. Amanda's mother makes her daughter promise she'll never talk about the troll outside of their family. Amanda slyly asks if the cat can stay and her mother allows it. Later that night the cat crawls into Amanda's parents bed where she's sleeping with them. She sees him & cuddles him.