By “popular songs” I mean to exclude campaign songs and any song that is just a list of the presidents. Also, the song has to refer to the President as a person – otherwise we could end up with hundreds of songs mentioning Washington, D.C.
Here are some I can think of:
George Washington – “Washington at Valley Forge” by Jim Kweskin
Abraham Lincoln – “Abraham, Martin & John” by Dion
Warren Harding – “Warren Harding” by Al Stewart
John F. Kennedy – “Abraham, Martin & John” by Dion
Richard Nixon – “Oh Mommy” by Brewer & Shipley
Richard Nixon – “Ohio” by C, S, N & Y
(I can’t stop you from just Googling a President’s name and “lyrics”, but if you can do it from memory, you’re obviously much cooler!)
Nixon is mentioned in David Bowie’s Young Americans.
From my school days, the group Up with people had a song called, Freedom isn’t free, with words “There was a man by the name of George, who led a small band of men at valley forge”
“LBJ” from Hair
“We’d Like To Thank You, Herbert Hoover” from Annie
ETA: Reagan gets a mention in Sting’s “Russians”. And Simply Red’s “Money’s Too Tight To Mention” refers to “Reaganomics”, which probably counts.