Ok, take your favorite band and you can only pick 3 songs off each of their albums,
and those are the only songs you can ever hear by that artist again, ever:

I'll start with U2 -

Boy - Into The Heart/Out of Control/The Electric Co.
October - Gloria/Tomorrow/October
War - Like A Song.../Surrender/"40" (I've heard SBS and NYD enough to last a lifetime)
The Unforgettable Fire - A Sort Of Homecoming/Pride/Bad
The Joshua Tree - Where The Streets Have No Name/With Or Without You/One Tree Hill
Rattle And Hum - Desire/Heartland/All I Want Is You
Achtung Baby - Until The End Of The World/Mysterious Ways/Acrobat
Zooropa - Zooropa/Lemon/Some Days Are Better Than Others
Pop - Do You Feel Loved/Mofo/Please
All That You Can't Leave Behind - Beautiful Day/Walk On/Grace
How To Dismantle An Atomic Bomb - Sometimes You Can't Make It On Your Own/City Of Blinding Lights/Crumbs From Your Table
No Line On The Horizon - No Line On The Horizon/Unknown Caller/Moment Of Surrender

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Just chillin' like Garret Quillin.

I'll sink my teeth into this a bit later but I love your inclusion of "Heartland", "Acrobat" and "Do You Feel Loved."

I am going to have to tackle this one tomorrow. Not sure I want to tackle the Bob Dylan catalog

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Flew too close to the sun on wings of pastrami

I'll do U2 later, but I'll start with my beloved Eagles for now...

The Eagles - Take It Easy/Witchy Woman/Peaceful Easy Feeling
Desperado - Tequila Sunrise/Desperado/Saturday Night
On The Border - Already Gone/James Dean/Best of My Love
One of These Nights - One of These Nights/Lyin' Eyes/Take it to the Limit
Hotel California - Hotel California/Wasted Time/The Last Resort (fuck that was a hard one)
The Long Run - The Long Run/In The City/Heartache Tonight
Hell Freezes Over - Get Over It/Love Will Keep Us Alive/Learn To Be Still (wasn't sure to include this but it did have some new material, so...)
Long Road Out of Eden - Waiting in the Weeds/Long Road Ot of Eden/Frail Grasp on the Big Picture (this may have been as tough for me as Hotel...)

Foo Fighters

Foo Fighters: I'll Stick Around, Big Me, For All The Cows
The Colour & The Shape: Hey Johnny Park!, My Hero, Everlong
There is Nothing Left to Lose: Breakout, Learning to Fly, Next Year
One By One: All My Life, Times Like These, Tired of You
In Your Honor: In Your Honor, No Way Back, DOA
Echos, Silence, Patience & Grace: Let It Die, Long Road to Ruin, Home
Wasting Light: Rope, These Days, I Should Have Known

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The Smashing Pumpkins:

Gish: Bury Me, Crush, Tristessa.
Siamese Dream: Hummer, Soma, Silverfuck
Pisces Iscariot: Frail and Bedazzled, Hello Kitty Kat, Obscurred (<---all time favorite TSP song).
MCIS: Disc 1. Jellybelly, Galapagos, Porcelina. Disc 2. Bodies, Thru the Eyes of Ruby, X.Y.U.
Adore: Crestfallen, Pug, For Martha
Machina: Everglasting Gaze, Stand inside your love, Try.
Machina 2: Glass, Speed Kills, Dross.
Zeitgeist: That's the Way, United States, Come on let's go.
Teargarden: Astral Planes, The Fellowship, Tom Tom.
Oceania: Pale Horse, The Chimera, Glissandra.

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@audioidkid

I know I already did the Eagles, but if I'm honest with myself, my favorite "band" (and I stretch the definition of that here, I'm sure) would have to be...

Marty O'Donnell and Michael Salvatori

Halo Original Soundtrack - Covenant Dance/On a Pale Horse/Halo
Halo 2 Original Soundtrack: Volume 1 - Ghosts of Reach/The Last Spartan/Earth City
Halo 2 Original Soundtrack: Volume 2 - Unyielding/Unforgotten/Finale
Halo 3 Original Soundtrack - Follow Our Brothers/One Final Effort/Wake Me When You Need Me
Halo 3 ODST Original Soundtrack - Overture/The Menagerie/Special Delivery
Halo: Reach Original Soundtrack - Overture/ONI: Sword Base/The Package

I'll cover Pearl Jam:

Ten - Release, Porch, Black
Vs. - Dissident, Blood, Rearviewmirror
Vitalogy - Corduroy, Last Exit, Nothingman
No Code - Sometimes, Smile, Red Mosquito
Yield - Brain of J, No Way, All Those Yesterdays
Binaural - Gods' Dice, Light Years, Grievance
Riot Act - All or None, Can't Keep, Save You
Self-titled - Comatose, Come Back, Inside Job
Backspacer - The End, Got Some, Unthought Known

Someone else can handle the hundreds of bootlegs.

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-- source

The Replacements:

Sorry Ma: "Takin' A Ride", "Customer", "I'm In Trouble"
Stink: "Kids Won't Follow", "Go", "Stuck In The Middle"
Hootenanny: "Color Me Impressed", "Within Your Reach", "Take Me Down to the Hospital"
Let It Be: "I Will Dare", "Unsatisfied", "Answering Machine"
Tim: "Bastards Of Young", "Left Of The Dial", "Here Comes A Regular"
Pleased To Meet Me: "Alex Chilton", "Can't Hardly Wait", "Valentine"
Don't Tell A Soul: "Talent Show", "Achin' To Be", "Rock 'n' Roll Ghost"
All Shook Down: "Merry Go Round", "All Shook Down", "Someone Take the Wheel"

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Don't take it personally.

Aerosmith

Aerosmith: Dream On, Mama Kin, One Way Street
Get Your Wings: Same Old Song and Dance, Seasons of Wither, Train Kept A Rollin
Toys in the Attic: Toys In The Attic , Walk This Way, You See Me Crying
Rocks: Last Child, Rats In The Cellar, Nobody's Fault
Draw The Line: Draw The Line, Kings and Queens, Milk Cow Blues
Night In The Ruts: No Surprize, Three Mile Smile, Remember
Rock In A Hard Place: Lightning Strikes.....uhhhh.....uhhhhhhh (God that album sucked)
Done With Mirrors: Let The Music Do The Talking, My Fist Your Face.......uhhh
Permanent Vacation: Hangman Jury, Rag Doll, Permanent Vacation
Pump: Young Lust, The Other Side, Monkey On My Back
Get A Grip: Cryin, Fever, Eat The Rich
Nine Lives: Nine Lives, The Farm, Hole In My Soul
Just Push Play: Beyond Beautiful, Sunshine, Avant Garden
Honkin On Bobo: Baby Please Don't Go, Stop Messin Round, The Grind,

Cool thread.

I'll go with Rage Against the Machine. I was late to the party with this group but became a fan after Audioslave formed. Now, I put RATM in my Hall of Fame.

Rage Against the Machine 1992: Freedom, Wake Up, Bullet in the Head
Evil Empire 1996: Bulls on Parade, Vietnow, Down Rodeo
The Battle of Los Angeles 1999: Maria, Calm Like a Bomb, New Millenium Homes
Renegades 2000: I'm Housin', The Ghost of Tom Joad, How Could I Just Kill a Man
Live at the Olympic Auditorium 2003: Born of a Broken Man, Calm Like a Bomb, I'm Housin'