Stars from New York, Hollywood and the music world gathered Sunday in Washington to salute the comedian and the band, along with Dustin Hoffman, Chicago bluesman Buddy Guy and ballerina Natalia Makarova.
The honors are the nation's highest award for those who influenced American culture through the arts. President Barack Obama will host the honorees at the White House before they are saluted by fellow performers in a show to be broadcast Dec. 26 on CBS.
Meryl Streep introduced the honorees Saturday during a formal dinner at the U.S. State Department and noted that Letterman had surpassed his mentor, Johnny Carson, in sustaining the longest late-night television career for more than 30 years.
Stephen Colbert and Jimmy Kimmel joined in celebrating Letterman's influence on many other comedians.
"I knew Johnny, and I loved Johnny. Johnny was beyond reproach," Colbert said in a toast to Letterman. "Dave was stupid. Dave was ours. Dave was like us.
"We wanted to throw things off of buildings. ... We would love to stick our heads out the window of 30 Rock and yell at passers-by, `I'm not wearing any pants!"'
Colbert marveled at Letterman receiving such an award after he "corrupted the minds of a generation."
Paul Shaffer, Letterman's longtime band leader, said he knew his boss was uncomfortable hearing such accolades, but that he knew Letterman was enjoying every second of it.
To salute Led Zeppelin, big names from the rock world dressed in black tie for their music heroes as a string ensemble played the band's hit song "Kashmir" and other tunes at the State Department.
Foo Fighters singer Dave Grohl said he never took any music lessons when he was starting out because "my teachers were Led Zeppelin. ... They were the most powerful thing in my life."
Lenny Kravitz said their influential music, at its zenith in the 1970s, became a lasting part of the culture of rock and roll.
"It's very difficult," he said. "You get four guys that come together and make something so much more powerful than they all are."
Zeppelin front man Robert Plant said he was flattered and overwhelmed in receiving the American culture prize. He said he was glad to see his former band mates, John Paul Jones and Jimmy Page, using good table manners.
The trio is scheduled to appear Monday on CBS' "Late Show with David Letterman." They are often asked if they'll reunite.
Plant told The Associated Press he plans to continue traveling the world and wants to make new music along the way.
"If anybody wants to write some new songs, I'm game to write songs," he said.
Hoffman was honored for charting his own path after taking a junior college class in acting that "nobody ever flunks." Streep, a 2011 honoree, said Hoffman's quest to become an actor required waiting tables and typing for the yellow pages by day.
"He'd do anything if it meant at night he could find himself on the stage," she said.
Glenn Close toasted Hoffman for defining the character actor as leading man in such movies as "The Graduate," "Rain Man" and "Tootsie" -- and as an artist who insisted on setting the highest standards for himself.
President Bill Clinton saluted Guy, the Chicago bluesman who was born into a family of sharecroppers with no electricity or running water in Louisiana. He went on to pioneer the use of distortion and feedback with his electric guitar.
"Buddy Guy's life is a miracle," Clinton said. "Just imagine you want to be a guitar player and you get your first strings by tearing off the screen door. ... He came from that to this."
Secretary of State Hillary Rodham Clinton said the ballerina Makarova "risked everything to have the freedom to dance the way she wanted to dance" when she defected from the Soviet Union in 1970.
Makarova quickly made her debut with the American Ballet Theatre and later was the first exiled artist to return to the Soviet Union before its fall to dance with the Kirov Ballet.
Clinton also took special note of Letterman, saying he must be wondering what he's doing in a crowd of talented artists and musicians.
"Dave and I have a history," she said. "I have been a guest on his show several times, and if you include references to my pant suits, I'm on at least once a week."
The crowd of artists and entertainers gave Clinton a standing ovation as she hosted her final salute to the nation's artists as secretary of State.
Kennedy Center Chairman David Rubenstein gave her a subtle nudge to run for president in 2016, saying there's another room at the State Department to name after a secretary who later becomes president.