The Beatles - Sgt. Pepper's Lonely Hearts Club Band
Featured on the cover are The Beatles (twice), Bob Dylan, Laurel and Hardy, Marilyn Monroe, Marlon Brando and many other icons of Pop Culture (as well as Stu Sutcliffe). The album won the Grammy for packaging (this year this Grammy was won by Aimee Mann). Ghandi, Jesus and Hitler were all removed before the final print. The album was released on June 1st, 1967 (June 2nd in the US) and was one of the first pop albums to have the lyrics printed on the cover (they're on the back).
Incidentally, I have this album cover framed and hanging on my wall, so it's appropriate to kick off the series with this one. Stay tuned for more.