So many things have been said about this band; definitely one of my favorites of all time; their classic singles are as powerful and wonderful as popular music gets. And while they'll never be as close to my heart as The Beatles, between Beggar's Banquet and Exile there was probably no finer band on the planet.
Interesting anecdote - I saw them one time only - in 1981, at the L.A. Coliseum, with the following opening acts: Prince, George Thorogood, and the J. Geils Band. Prince got booed off the stage, primarily by the asshole biker types I was unfortunate enough to be near, as they shouted, "Get off the stage, nigger!" Bill Graham came out and dressed the crowd down, saying something to the efeect of, "You're all a bunch of goddamn hypocrites! if it weren't for black music, none of you would be at this concert right now!" After which, Prince resumed playing a few more songs. George Thorogood - yawn. J. Geils - better, but still not killing me. Then The Stones come on, and with about a tenth of the equipment (and volume level) of the previous acts, swung like mad, and I understood why - even during a time when, even back then, people were grumbling about The Stones being past their prime - this band mattered so much; they simply rocked like fuck and swung in a way that more than made up for a lacklustre Mick Jagger.
Album - Sticky Fingers
Song - 'Monkey Man' (with an intro that rivals 'Gimme Shelter' and their most wicked groove/riff combination)