Originally Posted by +81

Alabama: Sun Ra
Alaska
Arizona: Andrew Jackson Jihad
Arkansas: Johnny Cash
California: Black Flag
Colorado: Christie Front Drive
Connecticut: Polaris (Adventures of Pete & Pete, yo.)
Delaware
Florida: Against Me!
Georgia: Circle Takes the Square
Hawaii: Pepper
Idaho: Treepeople
Illinois: Owls
Indiana: Ghost Mice
Iowa: Modern Life is War
Kansas: The Get Up Kids
Kentucky: My Morning Jacket
Louisiana: Acid Bath
Maine
Maryland: Dan Deacon
Massachusetts: Dinosaur Jr.
Michigan: Sufjan Stevens
Minnesota: Motion City Soundtrack
Mississippi
Missouri: Lucia Pamela
Montana: Steel Pole Bathtub
Nebraska: Elliott Smith
Nevada
New Hampshire: The Shaggs
New Jersey: Bubblegum Octopus
New Mexico: The Shins
New York: Sonic Youth
North Carolina: Catie Yerkes
North Dakota
Ohio: Devo
Oklahoma: The Flaming Lips
Oregon: Quasi
Pennsylvania: Black Moth Super Rainbow
Rhode Island: Lightning Bolt
South Carolina: James Brown
South Dakota
Tennesee: Jay Reatard
Texas: Butthole Surfers
Utah
Vermont: Johnny Hobo and The Freight Trains (a.k.a. Wingnut Dishwashers Union)
Virginia: Pig Destroyer
Washington: Melvins
West Virginia:
Wisconsin: Violent Femmes
Wyoming: Teenage Bottlerocket (though I don't listen to them much)
Washington, DC: Fugazi

This is the best I can come up with. Sorry lame musical states!