Consider this a public service announcement.
1) Salt of the Earth - Beggars Banquet (1968)
An anthem much in the style of The Band, basically making fun of working class people for being utterly powerless to change anything, and for being completely incomprehensible to the Stones.
2) Monkey Man - Let It Bleed (1969)
If the Red Hot Chili Peppers didn't listen to this song, it seems like they might have been able to avoid making everyone listen to Freaky Styley altogether. If they did, we can only be grateful that they took it to heart in the end. The slide guitar about 2/3 of the way through is super tight.
3) Street Fighting Man - Beggars Banquet (1968)
This song is not only amazing, but it was on their greatest hits CD, Hot Rocks. For some reason, though, I never hear anyone listening to it. Does everyone know this song? If not, then I just don't get it.
4) Sway - Sticky Fingers (1971)
This song is good for all the reasons that the Stones are good. I have no idea how this song is not popular, and Wild Horses is. The world is sometimes a cruel and arbitrary place.
5) Sing This All Together - Their Satanic Majesties Request (1967)
For some reason, I get the impression that indie hipsters haven't heard of this song. This is surprising, as it is not only right in the vein of some of the most paradigmatic indie music ever (i.e., Danielson), but also came way before a lot of the early heroes of the genre. This would suggest to me that they would be all over this shit. Go figure.
Out Of Control - Bridges to Babylon (1997)
I can accept that people don't listen to this, since really, who listens to stuff that the Rolling Stones made after Tattoo You? That being said, this song is really good, somehow reminding me of Black Magic Woman while still being clearly a Stones song.
Doo Doo Doo Doo Doo (Heartbreaker) - Goats Head Soup (1973)
This song combines Rolling Stones with an absurd disco horn line and somehow emerges sounding good. For that alone it deserves mention.