Some bands that come to mind..
Old school blues/garage rock:
Humble Pie
Canned Heat
J Geils
George Thorogood
Elvin Bishop,Bonnie Bramlett, the Allmans etc all had a southern-fried soulful bluesy sound, almost another category...
JJ Cale (he wrote Eric Clapton's hits After Midnight and Cocaine)
Check out his laid-back "Naturally" album and also the
fine album he recorded with Clapton just a couple years ago:
The Road to Escondido
JJ Cale's sound is a bit gentler, less raw than something like the White Stripes, leaning toward Americana--but still has that homey stripped down approach.
Newer school blues/garage:
Hives, Strokes (less bluesy, and I am really more familiar with the Strokes)
Kenny Wayne Shepherd ~ more southern accents--listen to Aberdeen
North Mississippi All-Stars ~ down-home
Derek Trucks - more finesse, but still very natural, organic sound
Newest garage sound, not so blues oriented:
Titus Andronicus ~ listen to A More Perfect Union
Lions Rampant