I got some grief from the Regular Son about my list of Stones' songs 11-20. He argues (probably correctly) that Happy is a greater song than Rocks Off, and that there's no way that Rocks Off is the 11th best Rolling Stones song, or even close (although it's a great song, no doubt). I guess that's what a list like this is for... generating discussion about something we both love. Sort of like arguing about who's better, Ruth or Gehrig, or Mays or Aaron, or Clemens or Maddux.
Anyway, moving on to the top 10, these should be a little less controversial, by which I mean that no one could possibly think they aren't great.
10. (tie) Street Fighting Man and Jumping Jack Flash.
Two great, great songs with classic Keith rhythm guitar lines. This is the Stones as they are entering their "golden age" in 1968... post-Brian Jones, post-psychedelia. This is the Stones doing what they did best... classic, tough, man-sized rock songs. As the Regular Son and I have commented, when the Beatles put these songs on the turntable and listened to them, this is about when they started to realize that the Stones were better than they were, and it wasn't close.
UPDATE: Here's a list published last summer from someone else. It's interesting to see what different people like... this guy's list, for instance, has songs in its top 10 that don't make my top 20, including Angie, Dead Flowers and Under My Thumb. All great songs, but just not my cups of tea. On the other hand, this guy also unaccountably leaves Satisfaction off his list of top 20 Stones songs. That can't happen and (spoiler alert) won't happen in my list. The greatest rock guitar riff ever has to be on the Stones' top 20 list, and near the top.