The awards are presented to people who have influenced American culture through the arts.
Meryl Streep introduced the honourees on Saturday during a dinner at the US 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.
Zeppelin front man Robert Plant said he was flattered and overwhelmed to receive 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.
Plant said he plans to continue travelling 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," said Plant, who collaborated with bluegrass singer Alison Krauss on the 2009 Grammy-winning album 'Raising Sand'.
Glenn Close toasted Hoffman for defining the character actor as leading man and for setting the highest standards for himself.