Excising future back & forth from the Memes thread.
Paul (McCartney) is Dead.
The story as I remember it was that on a rainy night in the late 60's (just prior to Sgt. Pepper), Paul is driving in his car and sees a young lady getting drenched. He pulls over to offer a ride and she accepts. As they resume, she realizes who she's in a car with and flips out. Paul loses control of the car and slams into a wall, killing himself and the girl.
The clues (not necessarily in order -
Abbey Road LP - The front cover shows George dressed as a common man/gravedigger. Ringo as a mourner. Paul, in the suit he crashed in as the dead man, he's out of step, shoeless and holding his cigarette in his right hand (he's left-handed). John as the preacher. The back of the album cover shows the wall the car slammed into. The crack in the wall runs through "BEATLES" indicating there's a fracture in the band.
Magical Mystery Tour - I Am The Walrus - In some Nordic mythology, the Walrus represents death. Strawberry Fields Forever - at the end it says, "I Buried Paul".
White Album - Glass Onion - the lyric "The Walrus was Paul" sung by John, admitting that Paul was dead (see: I Am the Walrus). Revolution #9 - playing the repeated words "number 9" in reverse sounds like "Turn me on dead man".
Sgt Pepper's Lonely Hearts Club Band - Front cover is Paul's grave. The guitar (in flowers) has four strings, Paul played a 4 string bass and faces with the fretboard to the right (as Paul would play left-handed). Paul holds an oboe across his body as one might when lying in repose in a casket. On the interior of the album, Paul has a patch on his shoulder that purportedly says, "OPD" (Offically Pronounced Dead).The "old Beatles" are in mourning (depicted). The back of the LP shows George, John and Ringo facing the camera with Paul facing away. George is making an L with his fingers, Paul's belt has a circle (an O), John has his hands tucked in his belt as a V and Ringo interlaced his fingers in an E (L-O-V-E). George's index finger also points to the lyrics of "She's Leaving Home" on the line "Wednesday morning at 5 o'clock...". Some DJ flipped the front of the album upside down & found that "BEATLES" looked like 537-1438, so he called the number on a Wednesday at 5 am and asked about the Beatles - the person who answered only said "PM". The DJ asked if the person could say anything more and the person said to call back later. The DJ checks the lyrics and finds "Friday Morning at 9 o'clock...", so he calls at that time and the number has been disconnected. In the song, "A Day in the Life" are the lines, "He blew his mind out in a car, he didn't notice that the lights had changed, a crowd of people stood and stared, they'd seen his face before...nobody was really sure if he was from the House of Lords", meaning his face looked familiar but was too messed up from the crash to identify.
Another part of the story has there being a "Beatles Look-alike" contest, hosted by a British Radio station with the winner getting some Beatles related stuff. The winner was a near match for Paul. His name was something like George MacKenzie. When Paul "died", the remaining Beatles grabbed him to fill in, despite his not knowing how to play any instrument. The rest covered for him on albums until they taught him how to play. Supposedly this happened before SPLHCB, which was why there was such a drastic change between it and the albums that came before. Someone even tried to do a dental comparison from photos, claiming that the Pauls had different smiles and tooth alignments.
I think there's more that I've forgotten. For their part, The Beatles claimed that they had no hand in the rumor or adding to it. A joke going around was that Paul's guitar playing "improved after he died". I personally don't think any of it is true, but I think the Beatles did play along to some extent. I'm pretty sure, that the patch that supposedly says "OPD" is actually "OBE" (Order of the British Empire)" award which they all received (and John returned).