“Big Rock Candy Mountain”. The version on the Oh, Brother, Where Art Thou? soundtrack, not the bowdlerized version they taught us in elementary school.
Lucinda Williams “Changed The Locks”. In fact, she says in the liner notes on the CD that she was specifically trying to write a song with no chorus.
They Might be Giants’ “Minimum Wage”. Two words, followed by a skillfully bad guitar solo.
More seriously, Queen’s “Bohemian Rhapsody” either has no chorus, or a bunch of different choruses.
Yes, they did. I would put Dylan’s “Tangled Up in Blue” and Springsteen’s “Jungleland” right there with the best of the non-chorus containing songs.
Jefferson Airplane’s White Rabbit