Loretta Claiborne, a former Special Olympics athlete and longtime friend of Shriver's, delivered welcoming remarks at St. Francis Xavier Roman Catholic Church.
"She was chosen to have a life to serve others, the weakest of the weak, the castaways, the throwaways of society, at the time they would say the mentally retarded, and I am one of those people," Claiborne said.
Shriver's grandchildren each offered prayers - giving thanks to her for teaching them to sail, for insisting girls are equal to boys, and for the lesson of helping those in need.
Shriver's daughter, Maria Shriver, and her son-in-law, California Gov. Arnold Schwarzenegger, and other family members carried the casket into the church after a funeral procession moved slowly past thousands of people who lined the streets. Shriver and Schwarzenegger were married in the same church 23 years earlier.
Shriver's husband, R. Sargent Shriver, a 1972 vice presidential candidate, also was at the service.
The crowds of people outside, including residents, tourists and Special Olympians, were largely silent for the procession as the church bell rang and a lone bagpipe whined.
The procession was led by law enforcers and athletes, including Marguerite Heffernan, of Harwich, a Special Olympian in 1968, and her 27-year-old son Shawn, from Orleans, who carried the Special Olympics torch.
"It was great," said Shawn Heffernan, who has won 49 swimming medals. "I'd done it before, but this was different."
His mother held her swimming medals from 1971 and recalled the impact Shriver had made on their lives.
"She helped open doors," she said. "We gained freedom from hiding."
The funeral Mass was shown live on television, but only those who were invited were allowed inside the church. Among the guests were Vice President Joe Biden, Oprah Winfrey, Jon Bon Jovi, Stevie Wonder and Massachusetts Gov. Deval Patrick.