There was such a mix of influences going on within The Band itself -- from Rockabilly to Motown -- with the big organ, Robertson's prickly guitar lines and Helm's raspy drawl -- and the great harmonies in the vocals. Certainly they influenced a lot of bar and club bands in the '70s and '80s, I think. Bands with a blues bent, many of which never -- or rarely -- recorded, let alone sold a lot of records. Check out the track "Dew Drop Inn" by the Downchild Blues Band, for instance.
Maybe another, more direct example -- "The Weight" by Jeff Healey.