I have a German shepherd, and along with the dust bunnies under my couch, I always find tufts of his hair. Every spring and fall he sheds profusely. He's nine years old now, and I have accepted life with “Dog Hair Everywhere”. I was recently asked about large or medium sized dogs that don't shed so profusely. Here are a few suggestions:
Standard Poodle

Be ready to laugh with this intelligent clown. Widely acknowledged as the Einstein of dogs, poodles are adept at learning tricks. They are also extremely versatile and can do just about anything that is asked of them. Do be aware though, they have a friendly, bouncy personality and their clownish attitude can sometimes make things interesting.
Bearded Collie
An ancient Scottish herding dog, the Beardie is loyal and intelligent. With his profuse coat and exuberant nature, he is often mistaken for an Old English Sheepdog with a tail. But a Beardie is not as large a dog.
The Bearded Collie Club of America writes that a Beardie is:
. . . a fuzzy, heart-warming hug!
. . . exasperating!!!
. . . a tail that can sweep a coffee table clean in an instant.
. . . eyes that can melt the heart, yet be full of understanding.
. . . a wet kiss with a beard fresh from the water bowl.
. . . knowing your kitchen floor will never again be totally dry.
. . . Bounce with a capital B!
. . . laughs for both owner and dog.
. . . an extraordinary memory.
. . . the ability to think and calculate.
. . . a puppy pout, always followed by forgiveness
Like most herding breeds, the Beardie does best when he has been assigned a job, and can spend time with his family.
A Beardie is double-coated and shedding is controlled with regular brushing.
Airedale Terrier

Theodore Roosevelt aptly described the Airedale as the breed that can "do anything any other dog can do, and then lick the other dog, if he has to."
The Airedale is the largest of all terrier breeds. His greater size embodies equally large devotion and courage while still being one of the calmest and most eager to please. He originating in the Valley of Aire in England, he is suspected to be a cross between the Old English Terrier, the Otterhound and other various Terriers, creating a hearty dog that quickly earned the title "Jack of All Trades".
The Airedale Terrier Club of America writes: “The Airedale enjoys being near his family and loves activity. Plentiful exercise in a safe area is very important. He can adjust to many environments and living situations. He has a jolly, friendly personality and although he will not back down if challenged, he is not generally a troublemaker and should get along nicely with other dogs. When he barks, there is usually a reason.”
This is a medium sized, handsome, sturdy dog with a wiry coat. Shedding can be reduced by regular grooming, in addition to regular weekly brushing and combing.
Portuguese Water Dog
The PWD is an ancient breed from, well, Portugal, but didn't make a real appearance in the USA until 1968. They were originally bred to accompany fishermen. They were hardy and great swimmers, capable of diving underwater to retrieve fishing gear. They are an exuberant, fun breed, and excel at agility, tracking, water work and other activities. Friendly by nature, they also make great therapy dogs.
PWDs are single-coated and considered to be hypoallergenic. Their coats are curly and do require grooming.
Soft-coated Wheaten Terrier

The AKC Breed Standard reads: “The Wheaten is a happy, steady dog that shows himself gaily with an air of self-confidence. He exhibits less aggressiveness than is sometimes encouraged in other terriers.”
This breed historically was an all purpose Irish farm dog and companion. They were bred to control vermin and guard their territory. They have evolved into a fun-loving companion animal and are usually good with children.
The coat is soft to the touch and requires grooming. Shedding is minimal with appropriate care.
Giant Schnauzer
A loyal and courageous working dog, the Giant Schnauzer is the largest version of the three Schnauzer breeds. He is extremely versatile, and excels at everything from agility to herding. He also makes a fine police dog and shines in the Schutzhund arena, but with appropriate socializing, is gentle with families and children. He weighs between 70 and 99 lbs, and needs vigorous exercise.
His coat is traditionally hand stripped, with a harsh outer coat and soft, dense undercoat. He requires regular grooming.
If you are looking for a non-shedding breed, consider adopting a mixed breed dog. Perhaps a mix of any of the above breeds would have the coat qualities you are looking for. A search on Petfinder could find you just the right thing.