As a lover of popular music (mainly 1960's) and also of music theory, I've always been especially fascinated by songs whose chord progressions are highly complex or unusual. Anyone could make a list of such songs by searching data bases of song titles, of course. But here are a few that stand out in my memory, without even using any lists. (I'm sure you'll have many more to add.) And if you look for them on "tabs" sites, remember that they don't always show the chords correctly -- especially with songs like these.
"I Am The Walrus": The Beatles used unorthodox chord sequences many times, but with this one they really pushed it!
"Friday On My Mind": First recorded by the Easybeats (from Australia) in 1967. It's sort of circular -- it seems to drift around from one key to another and back again.
"Lazy Day": The song by Spanky and Our Gang from 1968. Another song of the same "circular" type.
"Little Angel": The Four Seasons, in their golden years, had professional songwriters who often gave them a maze of chord changes. This one, though not well known, was an extreme case.
"The Anaheim, Azusa and Cucamonga Sewing Circle, Book Review and Timing Association": You wouldn't expect a complicated tune from Jan and Dean, but try this one. It's practically impossible to sing it alone without the music.
"Poor Old Mr. Jensen": Still less would you expect it from the 1910 Fruitgum Company! The progression in its bridge vaguely resembles one in a certain Beatles' song.
"Sleigh Ride": Leroy Anderson wrote this in 1948, without words, and it was a hit record by an orchestra. Later someone else wrote the words. Because it's so familiar, people often fail to notice the tune's complexity.
"My Hero, Zero": The song from "Schoolhouse Rock". This is a real chord maze! The original TV arrangement makes the chords inaudible. But check out the sheet music, or listen to the Lemonheads' recording.