I vaguely recall that it was either Fleetwood Mac or The Carpenters, but not 100% sure which one (if any).
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Clinton's well-known 1992 campaign theme song was Fleetwood Mac's 1977 hit "Don't Stop Thinking About Tomorrow," which gave the song new life, and convinced the group to briefly reunite for Clinton's inauguration. Clinton personally insisted on the song despite his advisors' doubts, so it's safe to call him a fan.
However, neither that song, nor anything else by Fleetwood Mac (or the Carpenters!) appears on Clinton's more recently revealed list of top 20 all-time favorite songs, which tends more towards gospel, jazz and folk than 70s rock.
Note, however, the song which inspired his daughter's name, the Judy Collins version of Joni Mitchell's "Chelsea Morning."
Mickey Magnum - "In The Presence Of Jehovah"
Miles Davis - "My Funny Valentine"
Nina Simone - "I Wish I Knew How It Would Feel To Be Free"
John Coltrane & Johnny Hartman - "My One And Only Love"
Zoot Sims - "Summertime"
Mahalia Jackson - "Take My Hand, Precious Lord"
Igor Butman - "Nostalgie"
Judy Collins - "Chelsea Morning"
David Sanborn - "Harlem Nocturne"
Phil Coulter - "The Town I Loved So Well"
Van Morrison - "Brown Eyed Girl"
Carly Simon - "I Get Along Without You Very Well"
Stan Getz with Bahai - "Charlie Byrd"
Simon & Garfunkel - "Bridge Over Troubled Water"
Sarah McLachlan - "Angel"
Elton John - "Philadelphia Freedom"
Willie Nelson - "A Song For You"
Joan Baez - "Winds Of The Old Days"
John Williams - "Concierto de Aranjuez"
Art Tatum - "There Will Never Be Another You"
The President's Own U.S. Marine Band - "Crown Imperial"
North Texas Wind Symphony - "English Folk Song Suite"
*Note: I was curious about this list, so I put together a YouTube playlist