These are all albums that I enjoy from start to finish. In no particular order:
Arcade Fire - Funeral, Neon Bible, The Suburbs
The Auteurs - After Murder Park
The National - High Violet, Alligator
The Beatles - Abbey Road, Sgt Pepper, Rubber Soul, The Beatles
Morrissey - Vauxhall & I, Bona Drag
Sigur Ros - Takk
My Bloody Valentine - Loveless
Pavement - Slanted and Enchanted
Sparklehorse - Vivadixiesubmarinetransmissionplot, Good Morning Spider
Elliot Smith - Either/Or, XO, From a Basement Up on a Hill
The Smiths - The Queen is Dead, Strangeways, Here We Come
Bob Dylan - Blood on the Tracks
Kanye West - My Beautiful Dark Twisted Fantasy
Wilco - Summerteeth, Yankee Hotel Foxtrot
Pulp - His n Hers, Different Class, We Love Life
Fiona Apple - The Idler Wheel...
Interpol - Turn on the Bright Lights
Jarvis Cocker- Jarvis
Joy Division - Unknown Pleasures
Bill Fay - Time of the Last Persecution
David Bowie - Hunky Dory, Ziggy Stardust, Station to Station, Heroes, Scary Monsters and Super Creeps
Radiohead - The Bends, OK Computer, Kid A, In Rainbows
I assume there's more that I can put on here but they escape me as of now.