The award is the nation's top prize for those who define U.S. culture through the arts.
Julia Roberts opened the show with a surprise nod to her friend, Winfrey.
"It's a universal conversation starter: Did you see what was on 'Oprah' today?" Roberts said. "The first time I heard of a better fitting bra ... or a fascinating politician named Barack Obama was on 'The Oprah Winfrey Show."'
For Winfrey, the prize comes during the 25th and final season of her talk show and just before she launches her new cable network, OWN, on Jan. 1.
"Simply put, she is the best interviewer ever," said Barbara Walters. "No one comes close - not even me. And those of you who know me know how painful it was for me to say that."
Alec Baldwin introduced the tribute for McCartney, 68, lamenting the singer's "long and winding road" to a solo career, being forced to sing in stadiums and requiring police protection.
"The National Institutes of Health called the epidemic Beatlemania," Baldwin said. "There was no cure."
The former Beatle was making his second visit to Washington this year for a culture award. In June, he won the Gershwin Prize for Popular Song from the Library of Congress.
A tribute to McCartney featuring some Beatles favorites brought out a special chorus that included Steven Tyler, James Taylor, Dave Grohl, Gwen Stefani and Norah Jones. They had McCartney - and the president - on their feet the entire time.
At a White House ceremony before the show Sunday, the honorees heard accolades from President Barack Obama who said the awards are important because the arts are necessary.
"The arts have always had the power to challenge and the power to inspire, to help us celebrate in times of joy and find hope in times of trouble. And although the honorees on this stage each possess a staggering amount of talent, the truth is, they aren't being recognized tonight simply because of their careers as great lyricists or songwriters or dancers or entertainers," Obama said. "Instead, they're being honored for their unique ability to bring us closer together and to capture something larger about who we are - not just as Americans, but as human beings."
At the gala performance, Angela Lansbury, Carol Channing and Kelsey Grammer performed some of Herman's famous tunes from "Hello, Dolly!," "Mame," and "La Cage aux Folles."
Channing, 89, who starred in "Hello, Dolly!" sang "Hello, Jerry." She said she knew it would make him cry.
Nashville turned out in force for Haggard's tribute. His all-star band included Willie Nelson, Sheryl Crow, Jamey Johnson, Kid Rock, Vince Gill and Brad Paisley.
Meanwhile, Jones was hailed as a rule breaker and revolutionary by playwright Edward Albee, Claire Danes and others.
Jones said he's often felt like an outsider, yet he's being honored for helping to shape the country. He said he could "feel the love" and that he was thrilled to be receiving the award while Obama is president.
The Associated Press contributed to this report.