I love the Stones -- in my book they're in the holy trinity of rock bands, along with the Beatles and Led Zeppelin. While I get the Beatles vs Elvis rivalry, and the fact that generally a fan falls into either one camp or the other but not both, I don't see that with the Beatles vs Stones. I don't relate to the idea of being a fan of one of these bands but not the other.
A previous poster mentioned "Wild Horses" and how it was about Mick's reaction to Marianne Faithfull's OD; I'd heard it was written by Keith and it was to his kids and how he felt when he left them to tour -- I'll have to look into that.
The Stones did something that in my opinion not even the Beatles topped, in that they released five consecutive albums which could be considered all-time greats: Beggar's Banquet, Let it Bleed, Get Your Ya-Yas Out (one of the all-time great live albums), Sticky Fingers and my favorite, Exile On Main Street. Exile is not that easily accessible, but on repeated listens it grows on you. Now I think there's not one weak song on the album.