Williams's songs include hits for Three Dog Night ("An Old Fashioned Love Song", "Family of Man", "Out in the Country"), Helen Reddy ("You and Me Against the World"), and the Carpenters ("Rainy Days and Mondays," "I Won't Last a Day Without You," and "We've Only Just Begun"). He wrote many songs with Kenneth Ascher, including "The Rainbow Connection", featured in "The Muppet Movie".