Bands whose entire studio album collection you own.

Sex Pistols
Public Image Ltd
Joy Division
The Doors
Play Dead
The Cult
Hanoi Rocks
Fields Of The Nephilim
The Mission
The Sisters Of Mercy
Flesh For Lulu
Skeletal Family
Lords Of The New Church
Siouxsie And The Banshees
Bauhaus
The Clash
Wasted Youth
Killing Joke
The Specials
The Ruts
The Stone Roses

 

Aimee Mann
Anne Bisson
April Wine
Badfinger
Big Star
Billy Squier
Black Sabbath
Boston
Cat Stevens / Yusuf
Colin Blunstone
Crowded House
Dan Fogelberg
Diana Krall
Eagles
Foreigner
George Harrison
Gordon Lightfoot
Ian / Iain Matthews
Jennifer Warnes
John Lennon
Led Zeppelin
Neil Young
Nirvana
Pink Floyd
Queen
Rachael Yamagata
Radiohead
Robin Trower
Roger Waters
Santana
Slade
T. Rex
Ten Years After
The Alan Parsons Project
The Beatles
The Doors
The Kinks
The Moody Blues
The Raspberries
The Zombies
Traffic
Wishbone Ash

 

Beatles
Paul McCartney
George Harrison
John Lennon
Big Star
Nick Drake
The Who
Simon & Garfunkel
Velvet Underground
Rodriguez
Tomorrow
The Leopards
Blue Things
The Remains

 

Me neither!

 

Off the top of my head and in semi-alphabetical order:

Arcade Fire
Bauhaus
The Beatles
Blur
The Cult
The Cure
The Doors
Gorillaz
Jane's Addiction
Led Zeppelin
Love and Rockets
My Bloody Valentine
New Order
Nirvana
Pearl Jam
Radiohead
R.E.M.
The Rolling Stones
The Smiths
Talking Heads
Tripping Daisy
U2
The Velvet Underground
The White Stripes

ETA: Oh, Big Star, too, now that you mention it.

 

Blind Faith.......

 

ABBA
Andrews Sisters
Asia (original lineup)
The Beatles
Black Sabbath (original lineup)
Boswell Sisters
CCR
Cream
Deep Purple
The Doors (original lineup)
ELO
Emerson, Lake & Palmer
Gillan
Grateful Dead
Jimi Hendrix (w/ Experience)
Buddy Holly & the Crickets
The Kingston Trio
Led Zeppelin
Lovin' Spoonful (original lineup)
Mamas and the Papas
Moody Blues (w/ Hayward/Lodge)
Rush
Simon & Garfunkel
Stray Cats
Yes

 

I have many artists whom I have the their entire studio output, however until extremely recently my Billy Joel collection consisted of Greatest Hits Vol 1, 2 & 3 and The Bridge.

Never once felt the need to buy anymore until I came back from a recent trip to NY. For some reasons his songs got stuck in my head (missed his MSG gig by a week) and so in one swoop, bought the whole damn lot on my return.

 

I MUST have the entire output of each and every band in my collection. And because I'm such a completist, I only collect records of bands with one album...

 

Not too many. Off the top of my head...
The Louvin Brothers
The Replacements
Simon & Garfunkel
The Velvet Underground
Wu-Tang Clan

 

Good one... I need to amend my list and add Blind Faith.

 

The Who
Oasis
Beatles
The Doors
Simon and Garfunkel
Chicago (original line up)
Al Kooper
Herb Alpert and the Tijuana Brass
The Dictators
Be Bop Deluxe
Ten Years After (original line up)

 

The Kinks (combo of CD, vinyl and downloads)
Small Faces (combo of CDs and vinyl)
Faces (vinyl and CDs)
Tom Petty (hi-res downloads)
The Who (hi-res downloads)
The Rolling Stones (combo of CDs and downloads, either hi-res or lossy)
George Harrison
Traveling Wilburys

 

The La's

 

<--------- among many others...

 

Beatles
John Lennon
Paul McCartney
George Harrison
Ringo Starr
Traveling Wilburys
Who
John Entwistle
Pete Townshend
Adele (she only has three)
Raconteurs (two albums)
Led Zeppelin (I have the box set)
Cream (also have the box set)
The Police (another box set)

Honorable mention:
Sex Pistols (they only had one)

I'm pretty close with a few others, like The Allman Brothers, Springsteen and Yes.

 

The Beatles
R.E.M.
Bruce Springsteen
Bob Dylan
Eagles
The Police
The Doors
U2
Grateful Dead
Van Morrison
Bruce Hornsby
Luka Bloom
Neil Young

 

The Police, The Beatles , The Monkees, and Bruce Springsteen

 

System of a down
The Jam
Rage against the machine

 

Buena Vista Social Club
Derek & the Dominos
Blind Faith
Marvin Gaye & Mary Wells
Jeff Buckley
Lauryn Hill
Stills-Young Band
Buckingham Nicks
Dennis Wilson
Hank Williams
Liz & Lisa
Buddy Holly
Tin Machine
Traveling Wilburys
Mudcrutch
Buffalo Springfield
Men At Work
Ben Folds
Til Tuesday
Andy Gibb
Jimi Hendrix
Janis Joplin
Crosby & Nash
Cream
David Gilmour

 

Hmmm. I might have missed a few out, or included a few that shouldn't be in but:

Alice In Chains (with Layne Staley)
Bush
Foo Fighters
Liam Gallagher
Noel Gallagher
Hole
Idlewild
The Jam
Mudhoney
Nirvana
Oasis
Red Hot Chili Peppers
Sex Pistols
Soundgarden
Stone Temple Pilots (with Scott Weiland)

 

There must be dozens of them if they only released a few albums.

 

Cheap Trick
The Beatles
Roxy Music
Bryan Ferry
Phil Manzanera
Miles Davis
John Lennon
Paul McCartney
George Harrison
The Police
XTC
Translator
Poco
Pink Floyd
Martin Newell (and The Cleaners From Venus)
Love
Moby Grape
The Who
CCR
ZZ Top
Laura Nyro
Pete Townshend
John Entwistle
ELO

There's more.

 

What I personally own and bought with my own money and have on physical format (CD or Vinyl):

Judas Priest
Iron Maiden
Metallica
Overkill
Grave Digger
Iced Earth
Blind Guardian
Demons And Wizards
Jag Panzer
DragonForce
Rush
Queen
The Cars
U2
Van Halen
AC/DC
Guns N Roses
The Rolling Stones
Led Zeppelin
The Doors
The Who
Creedence Clearwater Revival
The Beatles
Pink Floyd
Jimi Hendrix
Elvis Presley
Michael Jackson
John Mellencamp
Billy Joel
John Lennon
John Fogerty
Lady Gaga

Probably a few others I can't think of right now.

Also, I have near completions of a few other artists, such as Paul McCartney, Billy Idol, James Taylor, Styx, Cheap Trick, Megadeth, Ozzy, Dio, Black Sabbath (though got all Ozzy-led, RJD-led and even a few of the others with other singers)


Now if I count lossless copies of artists that I obtained by other means, that list would skyrocket. But I am not counting any of those.

 

The Band,The Beatles,Buffalo Springfield,The Yardbirds,Faces,Delaney & Bonnie,CCR, that might be about it.