Robert Plant has come to abhor the band's classic song, "Stairway to Heaven" - and refuses to play it in concerts. His lengthy refusal to take part in a Led Zeppelin reunion was due to his disgust with the fact that he would inevitably be forced to sing it.
Jimmy Page has also stated that he hates "Living Loving Maid (She's Just a Woman)", saying it was just written as filler note It probably didn't help that his girlfriend ended up hating it as well and making it one of the few Led Zeppelin songs never performed live. Doesn't stop classic rock stations from keeping it in heavy rotation to this day (usually following "Heartbreaker", since there was no real gap between the songs on the original album).
Then, to round things out, John Paul Jones is said to have never been too fond of the song "D'yer Mak'er".
That leaves John Bonham as the only member who had no dislike for something.
Hipgnosis did the cover art for Houses of the Holy, Presence, The Song Remains the Same, In Through the Out Door and Coda.
The alleged Satanic messages when "Stairway to Heaven" is played backwards.
Another rumor about the band is that the members sold their souls to Satan in exchange for fame and fortune, and John Paul Jones was the only one who refused, which is why Jones is the only member of Led Zeppelin who hasn't suffered a horrible tragedy in his life.
Zepp - or at at least, Peter Grant - turned down an invitation for the band to perform at the original Woodstock.
A tour planned in August 1975 got cancelled when Robert Plant got injured in an accident in Greece. The group recorded Presence instead.*
The planned XYZ project with Page, Plant, and Yes's rhythm section Alan White and Chris Squire. Didn't happen due to Plant's grief over Bonham's death and his dislike for the complexity of the music. It eventually turned into Yes's later reunion and 90125 album. Page did perform with Yes at one show in 1984 (although I'm unsure if any recording of this show exists), and a demo tape of XYZ material can be found on the internet.