Realizing the children were far more capable of sports than experts said, Shriver organized the first Special Olympics in 1968 in Chicago.
The two-day event drew more than 1,000 participants from 26 states and Canada.
By 2003, the Special Olympics World Summer Games, held that year in Dublin, Ireland, involved more than 6,500 athletes from 150 countries.
The games are held every four years.
Well into her 70s, Shriver remained a daily presence at the Special Olympics headquarters in Washington.
Juvenile delinquency was another issue that interested Shriver and spurred her to action. In his 1991 book "The Promised Land: The Great Black Migration and How It Changed America," author Nicholas Lemann said the Kennedy administration's juvenile delinquency commission, "a pet project that had been created to placate Eunice," became the precursor of the vast federal effort to improve the lot of urban blacks.
After he took office, President Lyndon B. Johnson tapped R. Sargent Shriver to lead his War on Poverty.
Eunice Shriver was the recipient of numerous honors, including the nation's highest civilian award, the Presidential Medal of Freedom, which she received in 1984. In May, the National Portrait Gallery installed a painting of her—the first portrait commissioned by the museum of someone who had not been a president or first lady.
Shriver was born in Brookline, Mass., the fifth of nine children to Joseph P. Kennedy and Rose Fitzgerald Kennedy. She earned a sociology degree from Stanford University in 1943 after graduating from a British boarding school while her father served as ambassador to England.
She was a social worker at a women's prison in Alderson, W.Va., and worked with the juvenile court in Chicago in the 1950s before taking over the Joseph P. Kennedy Foundation with the goal of improving the treatment of the mentally disabled. The foundation was named for her oldest brother, Joseph Jr., who was killed in World War II.
In 1953, she married Shriver. He became JFK's first director of the Peace Corps, was George McGovern's vice-presidential running mate in 1972, and ran for president himself briefly in 1976.
Survivors include her husband, who was diagnosed with Alzheimer's disease in 2003, and the couple's five children: former NBC newswoman Maria Shriver, who is married to Schwarzenegger; Robert, a city councilman in Santa Monica, Calif.; Timothy, chairman of Special Olympics; Mark, an executive at the charity Save the Children; and Anthony, founder and chairman of Best Buddies International, a volunteer organization for the mentally disabled.
Mark Shriver once said his parents' actions, not just words, influenced their children.
"In the course of our upbringing, they stressed the importance of giving back," he said. "But we didn't sit around having family discussions about it. We learned by what she and my father were doing."