Recipients included singer Neil Diamond, cellist Yo-Yo Ma, actress Meryl Streep, Broadway singer Barbara Cook and jazz saxophonist Sonny Rollins.
The nation's top award is given to those who have influenced American culture through the arts.
"They have different talents, and they've traveled different paths," said President Obama. "And yet they belong here together because each of tonight's honorees has felt the need to express themselves and share that expression with the world."
Smokey Robinson paid special tribute to Diamond with a rendition of "Sweet Caroline," and Nora Ephron suggested Streep play the role of Hillary Rodham Clinton in her next film.
Ephron said Streep's talent, versatility and resemblance to Clinton made it "inevitable" that she would one day play the secretary of state and former first lady.
Clinton laughed, while Streep jokingly stood up for a better look at the nation's top diplomat.
Caroline Kennedy, who hosts the show, acknowledged her personal connection to Diamond, saying he was "a Brooklyn lad with a gift of melody who grew into a solitary man, 'reaching out, touching me.'"
The song is a story about Diamond's former wife, but he took the name from Kennedy.
Stephen Colbert made a surprise appearance with Elmo from TV's "Sesame Street" to honor Ma, who is one of the best-known classical musicians.
"Tonight we celebrate the greatest living cellist," Colbert said "We chell-ebrate, if you will."
The Associated Press contributed to this report.