More than 10 years ago, when Wendelyn Galligan of Edgartown first brought a chihuahua home, she was greeted with a cat paw-adorned sign, hung near the door by her husband, that read “No Dogs Allowed.” When Ms. Galligan showed her spouse Billie Taco, their new rat-like puppy, he exclaimed, “Where did you get that from, the Edgartown dump?”

Today a very different sign welcomes visitors to the Galligan residence. It is a green imitation street sign inscribed with white letters that read, “Chihuahua Court.” Now 11-year-old Billie Taco has two other chihuahua companions, Jazmine and Eli.

Whether it is forced upon them or they are born with it, it’s safe to say that most Vineyarders are besotted with dogs.

There are 2,791 sets of furry paws registered to owners living in Edgartown, Oak Bluffs, Tisbury, West Tisbury and Chilmark, according to town records.

Edgartown is home to 895 pooches, more than in any other Vineyard town. Golden retrievers are the most popular breed on the Island, followed by black and yellow labs. The most common Vineyard dog name is Molly, followed by Max and Lucy.

Vineyard pooches are notable for exotic names, too. Jake the Snake, Snapdragon and Kabookie live in Edgartown.

A shih tzu named Chiyo-chan, a Jack Russell terrier named Blood Fang and a bichon frise named Rock & Roll reside in Oak Bluffs.

Captain Bubba McLovin, an English bulldog, and Tebucky Jones, a Boston terrier, live in West Tisbury. There is a golden lab named D.O.G. in Tisbury and a golden retriever named Julee Mango in Chilmark.

ZuZu Smooth, a shaggy three-year-old shih tzu belonging to Neale and Ellie Bassett of Edgartown, earned the first portion of her name from a movie character named Zuzu, the little girl who helps bring her father back to life in the film It’s a Wonderful Life. The latter portion of the pup’s name, Smooth, memorializes Ms. Bassett’s favorite word and her favorite Carlos Santana song.

With the spirit and size of a Tickle-Me-Elmo doll, ZuZu Smooth beams with glee. She prances, she trots, she hops and she slides — saying hello, roughhousing a stuffed green frog or chasing a speck of red light from a laser pen.

“We didn’t train her to do anything cute, that is just a natural expression of her joy,” Ms. Bassett says, teasing Zu with lion-like growls. After the woman and her pup play, Zu hugs her paws around her owner’s forearm. “She’s trying to say how happy she is to see you and it breaks your heart, it’s so cute.”

Zu is pampered like a princess. She is groomed once a month, bathes every two weeks, takes five walks each day and wipes her paws before galumphing back inside the house. She eats all-natural dog food — never table scraps — and sleeps sprawled between her owners in bed, propped upon a pillow.

“We should all take a lesson from her,” Ms. Bassett says. “She’s happy and she sleeps all the time. Her only goal is just to play — that’s all she wants to do. And then when she has to, she eats. And when she has to, she drinks. She’s always ready to play. I don’t know why we humans can’t get there.”

Many Vineyarders name their pooches after the Island itself. The most popular Island-inspired pup name is Chappy. The Vineyard is also home to pups named Katama, Lambert and Lucy Vincent. There is a four-legged Aquinnah in Tisbury, a yellow lab named Edgar in Edgartown, yet just one Martha, residing in Chilmark, on the Island.

A three-year-old cocker spaniel named OB lives in Oak Bluffs with John and Jeanne Rogers and their two eight-year-old children.

“We love the town,” Ms. Rogers says, petting her freshly bathed dog. “He’s OB from OB.”

Rich brown fur surrounds OB’s eyes like a masquerade mask. It covers his floppy ears, speckles the tip of his snout and forms a perfect circle the circumference of a CD above his left shoulder. OB’s cottonball tail and the rest of his coat are shiny and white. His tongue emerges from his mouth like a handshake, greeting palms, cheeks, mouths, doggy treats and chair legs with a doting, sloppy lick.

“Dogs are such an integral part of the Island’s fabric,” Mr. Rogers says. “There are so many dog parks here — that’s the lure and the charm of the Island.”

On a Sunday evening in Trade Winds dog park in Oak Bluffs, a slender silver-grey weimaraner named Rigby and a coonhound named Cashmere trot along a wooded path. The dogs’ owner, Oak Bluffs selectman Ron DiOrio, trails behind, musing about the Island’s affinity for dogs. “It’s the laid-back style of the life here,” Mr. DiOrio says. “People here are very accepting of animals on the Vineyard, especially of dogs.”

Much of the Vineyard travel and tourism industry caters to dogs. Aside from trails and parks plotted especially for dogs, many Vineyard shops, restaurants and lodgings are critter-friendly. The Steamship Authority allows leashed dogs to travel aboard its ferries for free. Aboard Cape Air, passengers’ furry friends can fly cageless in their laps.

To many Vineyarders, dogs are like children. Whether leashed at their side, perched on their lap for an airplane ride to Nantucket, or sprawled on the passenger seat of their car, dogs accompany their owners everywhere.

Alice VonWolftrap is a five-year-old German shepherd-Portuguese rabbit hound mix belonging to Trina Kingsbury of Chilmark. Alice is Trina’s companion, friend and family.

“She’s got the beard of a goat, the back and the bristles of a pig, she’s sprouting fur on her feet like a Clydesdale [horse], [she has] the tail of a big rat, with one ear up [and] one ear down — the dog is fug, a fuzzy ug,” Ms. Kingsbury says with a crackling laugh.

Ms. Kingsbury saved Alice when she was about to be put to sleep as a vicious four-month-old pup. Alice, she says, acted out because she had been caged and abused.

“I said, ‘She’s not vicious, she’s been mistreated. Just like children, if you mistreat a child, they’re going to react. Old Newton’s theory,’” Ms. Kingsbury says adding:

“I forced her to fall in love with me. Those beautiful brown puppy eyes on this terrified animal — I just stared at her and stared at her and stared at her until she fell in love with me. I was sending vibes back: I love you, you furry bag of fluff. You’re going to come home with me, you’re going to be good, no one is going to hurt you again . . . And she did, she fell in love with me. And she’s a good dog.”

To compensate for Alice’s trauma-stricken puppyhood, Ms. Kingsbury spoils her dog. Alice sleeps curled on a miniature brass bed atop a feather mattress and a hand-crocheted coverslip. She also has a miniature kitchen set, complete with hanging brass pots and pans and a tiny wind-up Dirt Devil vacuum cleaner that she chases like a ball. Alice even has her own car, an old golf cart refurbished with red naugahyde seating and black plastic beading. Ms. Kingsbury drives Alice, ears flapping in the breeze, in the passenger seat of the “little surry” to greet the neighbors.

“I say to people, ‘You do this for your children right? Don’t they have bicycles and wagons and their own little chairs? Well, I don’t have children, I have my animals!’”

Alice is so popular that she wins more hellos from neighbors and friends than Ms. Kingsbury. The 2005-2006 Island phone book listed Alice VonWolftrap as a resident of her owner’s home.

Ms. Kingsbury also cares for a 17-pound Maine coon cat she calls Tossu, a nickname for Star Pikku Tossu II, which means “little slipper” in Finnish. Orange, longhaired Tossu and Alice are an unlikely yet inseparable duo. They are always together, playing and protecting one another.

“At the end of the day, by the firelight, just looking at these little fuzz-buckets curled up together,” Ms. Kingsbury says. She sighs softly. “Thank God for the animals.”