My choices, like some others have stated, are based on an albums importance, but also on the visual impact of the artwork, rather than on my own opinion of the records relative quality. Although these are all records I like.
The Beatles Abbey Road
The last record the Beatles made together was marked the symbolic end of a musical era. The cover is uniquely English, and it also shows the four members, looking more like individuals than a band, going somewhere. Heading to the studio for a session perhaps, or on their way to the next chapter in their lives. Obviously Sgt. Pepper, Revolver and even The White Album in its way were great album covers, but when someone mentions the Beatles to me, this is the image that flashes through my mind.
The Rolling Stones - Sticky Fingers
The famous Andy Warhol cover managed to convey sexiness, playfulness and mystery all in a single image. If Abbey Road marked the end of the 60's, Sticky Fingers marked the start of the 70's.
Bob Dylan - The Freewheelin' Bob Dylan
The early sixties youth movement captured in a single image. It displayed the promise of freedom the lie beyond the borders of suburbia. It's a perfect little time capsule of Bohemian New York.
Pink Floyd - Dark Side of the Moon
Simple yet powerful. It conveys the meeting place between beauty and design, art and science, intellectualism and aesthetic. No album cover is a more succinct representation of the music it contains.
Bruce Springsteen - Born to Run
Clad in leather and Telecaster, he's the ragamuffin hero of his own romantic opera. His smirk suggests he just told Clarence "Wait'll they hear this!"
The Clash - London Calling
While the Sex Pistols could be dismissed as a trendy novelty, The Clash announced British punk was for real by releasing its first great album. The iconic cover shows Paul Simonon ring the bell to announce their arrival by beating the stage with his bass.
Nirvana - Nevermind
Without question a game changing record that brought rock back, briefly, from the brink of market researched homogenization. The cover was a simple idea that conveyed a powerful message. That greed is trained straight out of the womb.