This is an extremely difficult list to compile. The main problem is that in my not so humble opinion practically no artist or band has made the perfect album, not even The Beatles, not even Miles Davis or David Bowie. There's always a flaw somewhere, always at least one track that's a bit dodgy, often a superfluous reference to gods or prophets, often a few things that just don't work .

Not even compilation albums can cut it - there's always at least one poorly chosen track, even if the relevant artists made the choices themselves (which is rare).   

These are my favourite albums, all of them "close calls" to my idea of perfection. There might even be some correlation to frequency, i.e. the more often you've heard this stuff, the higher your awareness of it ... more  Eventually I will provide reviews of my own, reviews by others, links to album covers and, barring legal complications, samples of the music.
For the moment, you'll have to be satisfied with a few funny pictures, animations and links to websites.
UC
UC2
Back To What I Like
Bob Dylan - Bringing It All Back Home
John Martyn - Grace And Danger
Jefferson Airplane - Surrealistic Pillow
Skeleton
Van Morrison - Astral Weeks
The Style Council - Café Bleu
Frank Zappa - Overnite Sensation
John Lennon - Imagine
Love - Forever Changes
Del Amitri - Change Everything
Prefab Sprout - Steve McQueen
Neil Young - After The Goldrush
The Beatles - Abbey Road
Bob Marley - Exodus
Joni Mitchell - Hejira
Jimi Hendrix - Are You Experienced?
Pink Floyd - Dark Side Of The Moon
Santana - Abraxas
The Doors - The Doors
Elvis Costello - My Aim Is True
David Bowie - Ziggy Stardust
Quicksilver Messenger Service - Happy Trails
Cowboy Junkies - The Trinity Session
Sade - Lovers Rock
The Blue Nile - High
The Grateful Dead - American Beauty
Smiley
BlueFlash