Wikipedia has an extensive list, from which I've extracted some of the names I recognize:
Alan Alda born 1936 An actor most famous for his role as Hawkeye Pierce in the television series M*A*S*H. Alda contracted polio at age seven, during an epidemic. His parents administered a painful treatment, developed by Sister Elizabeth Kenny, in which hot woolen blankets were applied to the limbs and the muscles were stretched by massage
Mia Farrow born 1945 An actress who was appointed a UNICEF goodwill ambassador in 2000, and campaigns in the fight against polio. Farrow collapsed on her ninth birthday and was diagnosed with polio two days later. She was in the hospital for eight months, where an iron lung maintained her breathing.
Gwen Verdon 1925–2000 An actress and dancer on Broadway and in films. Verdon was encouraged to dance by her mother, a dance teacher, as therapy for her polio-afflicted legs.
Johnny Weissmuller 1904–1984 At age nine, Weissmüller contracted polio. At the suggestion of his doctor, he took up swimming to help battle the disease, and he went on to win five Olympic gold medals in the sport during the 1920s.
Arthur C. Clarke 1917–2008 A science-fiction author and inventor. He contracted polio in February 1962, which confined him to bed for months. In 1984, he was diagnosed with post-polio syndrome, and he spent the last years of his life in a wheelchair.
Judy Collins born 1939 As a child, singer-songwriter Judy Collins spent several months in the hospital recovering from bout with polio. Collins later became a representative for UNICEF and has worked to promote polio vaccination programmes.
Donovan born 1946 Folk singer-songwriter and guitarist Donovan contracted polio, aged four, from the vaccine he was given. This left him with a limp and feeling excluded. However, he says "I kind of look back on it and think it was positive for me because it made me withdraw from my pals and realise I was different."
Michael Flanders 1922–1975 An actor, broadcaster, and writer and performer of comic songs, often in partnership with Donald Swann. He contracted polio in 1943 while serving in the Royal Navy, and required a wheelchair for the rest of his life.
Joni Mitchell born 1943 A musician, songwriter and painter. Mitchell started singing at age nine while in the hospital recovering from polio. Her distinctive sound featured dozens of non-standard guitar tunings, which she developed partly to compensate for a weakened arm.
Itzhak Perlman born 1945 A virtuoso violinist. He contracted polio at the age of four. Perlman requires braces and crutches to walk, and plays the violin seated.
Dinah Shore 1916–1994 A big band singer, actress and talk show host. Shore contracted polio, aged 18 months, which left her right leg crippled. She recovered strength through massage, swimming and tennis.
Neil Young born 1945 A singer-songwriter and guitarist. He caught polio at age five, during the epidemic of 1951.
Mitch McConnell born 1942 A Republican member of the United States Senate from Kentucky and current Senate Minority Leader. He contracted polio at age two resulting in a paralyzed left leg, but eventually recovered with physical therapy.
Robert McNamara 1916–2009 A business executive and former United States Secretary of Defense. Both McNamara and his wife contracted polio in August 1945. He was in the hospital for a couple of months but his wife was badly affected and remained there for nine months. His career change from Harvard professor to the Ford Motor Company was made to pay her hospital bills.
Franklin D. Roosevelt 1882–1945 U.S. President 1933-1945. FDR founded the National Foundation for Infantile Paralysis, now called the March of Dimes. He spent as much time as he could recuperating from Poliomyelitis in the waters of Warm Springs, Georgia where he founded one of the first rehabilitation facilities for Polio survivors.
Bud Grant born 1927 The long-time former American football head coach of the Minnesota Vikings of the National Football League for eighteen seasons. He caught polio as a child, leaving one leg shortened. He was advised to take up sport as therapy.
Jack Nicklaus born 1940 A professional golfer who has won many major golf championships. He caught polio, aged 13. Nicklaus was affected with stiffness, pain and weight loss over two weeks. He recovered without any paralysis but believes he may have post-polio syndrome, which makes his joints sore.
Wilma Rudolph 1940–1994 A track and field athlete, Rudolph was the first American woman to win three gold medals at the Olympic Games. At age four, she contracted polio and lost the use of her left leg. After five years of massage and exercises, she managed to walk again without her leg braces. By the time she was a teenager, Rudolph was faster than the boys in her neighbourhood were. Rudolph won a bronze medal, aged 16, at the 1956 Summer Olympics and three gold medals in the 1960 Summer Olympics.
Frida Kahlo 1907–1954 A painter who was the subject of a 2002 movie starring Salma Hayek. She caught polio, aged six, and spent several months in bed. Kahlo was left with a deformed and shortened right leg.
Dorothea Lange 1895–1965 A photographer and photojournalist most noted for her picture Migrant Mother. She caught polio, aged seven, and was left with a withered right lower leg and a limp. Lang said, "It was perhaps the most important thing that happened to me. It formed me, guided, instructed me, helped me, and humiliated me. All those things at once. I've never gotten over it and am aware of the force and power of it."
Henriette Wyeth 1907–1997 A portrait artist. She caught polio as a child, which crippled her right hand. She compensated by holding the paint brush between her first and second fingers.