Arcade Fire - Funeral
New Pornographers - Mass Romantic
Islands - Return to the Sea
Lupe Fiasco - Food and Liquor
Kanye West - College Dropout
Band of Horses - Everything All The Time
The Decemberists - Castaways and Cutouts
Portishead - Dummy
65daysofstatic - The Fall Of Math
Weezer - Weezer
Nas - Illmatic
The Mars Volta - Deloused In The Comatorium
Third Eye Blind - s/t
Jeff Buckley - Grace
Rage Against the Machine - Rage Against the Machine
Battles - Mirrored

Black Crowes - Shake Your Money Maker
The Eagles - The Eagles
Dr. Dre - The Chronic
Snoop Doggy Dogg - Doggystyle
Eminem - The Slim Shady LP
Aerosmith - Aerosmith
Led Zeppelin - Led Zeppelin
Boston - Boston
Montgomery Gentry - Tattoos & Scars
Dixie Chicks - Wide Open Spaces
Gretchen Wilson - Here For The Party
Garth Brooks - Garth Brooks
Trisha Yearwood - Trisha Yearwood

Appetite for Destruction
Exile in Guyville

Weezer - Weezer
Rage Against The Machine - S/T
Led Zeppelin - Led Zeppelin

The Band - "Music From Big Pink"

Lynyrd Skynyrd - "Pronounced Leh-Nerd Skin-Nerd"

R.E.M. - "Murmur" (...that is assuming EPs don't count for this)

The Who - "The Who Sings My Generation"

Jimi Hendrix - "Are You Experienced?"

Aside from some already mentioned...







All within about two years of each other as well...

Van Halen
Montrose
Allman Bros.
Bad Company
Blue Oyster Cult
Captain Beyond
Joe Cocker!
Crosby Stills Nash
Foreigner
Heart-Dreamboat Annie
Steely Dan-Can't Buy A Thrill
Molly Hatchet
Hendrix-Are You Experienced?
Rush
Santana
Supertramp-Crime of the Century
King Crimson-In The Court of the Crimson King
Foghat

Now that one I would debate. I love Rush, but I consider their debut album nearly totally unlistenable.

Pearl Jam's first album is actually the first one that came to mind for me. Also, after looking through my cd's: Men At Work and Violent Femmes.

Definitely. First one that came to mind as well. Boston is another great one.

KISS (of course)
Nine Inch Nails
Suede (or London Suede as they were known over here in the US)
a-ha
Sex Pistols
The Killers
Pet Shop Boys
Prick

(also previously mentioned Cars, Boston, Foreigner)

The Stone Roses
Nine Inch Nails - Pretty Hate Machine
Beastie Boys - License To Ill
Ned's Atomic Dustbin - God Fodder
U2 - Boy
Enigma - MCMXC a.D.
Jane's Addiction - Nothing's Shocking
Joy Division - Unknown Pleasures
Moby
Scissor Sisters
Sigue Sigue Sputnik - Flaunt It
Pete Yorn - Musicforthemorningafter

Gaslight Anthem - Sink or Swim

First of all, I agree with Randy Miller on his picks of Bjork and Belle and Sebastian (my favorite band). The pic for his 2nd selection isn't showing up, but we seem to share musical tastes.

Some others I'd like to note:

Nick Drake - Five Leaves Left
Oasis - Definitely Maybe
Sparklehorse - Vivadixiesubmarinetransmissionplot
The Stone Roses - The Stone Roses

Van Halen - Van Halen
The Jimi Hendrix Experience - Are You Experience
Led Zeppelin - Led Zeppelin
Sex Pistos - Never Mind the Bollocks (actually their only record)
Pearl Jam - Ten
The Stone Roses - The Stone Roses
Elastica - Elastica
The Velvet Underground - The Velvet Underground and Nico

Pearl Jam's Ten was the first record to come to my mind, too.

I agree with lots of the ones above, here's some more. There are also basically bands that emerged fully developed on their first album:

Cheap Trick: S/T (and the rapid-fire subsequent three studio albums)
The Stooges: The Stooges
Roxy Music: S/T
The Byrds: Mr. Tamborine Man
Violent Femmes: S/T
Chemical Brothers: Exit Planet Dust
Beck: Mellow Gold
The Smiths: S/T
Echo and the Bunnymen: Crocodiles
Lloyd Cole: Rattlesnakes
The Gun Club: Fire of Love
Talking Heads: '77
The Streets: Original Pirate Material
The Orb: The Orb's Adventures Beyond the Ultraworld

Recently (since 2000):

Arcade Fire — Funeral
Badly Drawn Boy — Hour of the Bewilderbeast
Coldplay — Parachutes
Maxïmo Park — A Certain Trigger

Others can mention older albums, as I would be unable to frame them in their proper historical context.

The Stone Roses self titled debut
REM - Murmur
Belle & Sebastian - Tigermilk
Radiohead - Pablohoney
Velvet Underground with Nico self titled
Coldpaly - Parachutes

Ramones

Kate Bush



The Clash




The Auteurs




Aztec Camera




Big Country




Graham Parker




Elvis Costello




Rockpile




Microdisney




The Jam




Tom Robinson Band

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How could I forget Guns N' Roses - Appetite for Destruction? I bought that damn CD 5 or 6 times.

Pearl Jam - Ten
Joe Stummer & The Mescaleros - Rock Art & The X-Ray Style
Iron Maiden - s/t
The Clash - s/t
GNR - Appetite
Motley Crue - Too Fast For Love

One and only albums:
Operation Ivy "Energy"
Havana 3 AM - s/t