Well, the most of the time I listen to seventie's Rolling Stones' songs, not from these years. I'm not a big fan of this band, I mean, I love their music but I don't know what they have done recently.
Rough Justice, Let Me Down Slow, Oh No Not You Again (I was a fan of A Bigger Bang); anything off the new rarities Exile disc if you haven't already heard that; Highwire.
And I know its not recent and not technically 70s but Tattoo You has some great stuff. Hang Fire, Start Me Up obviously.
A list of worthwhile songs from this period include:
Mixed Emotions Terrifying Almost Hear You Sigh Slipping Away Love Is Strong You Got Me Rocking Out of Tears Baby Break It Down Flip the Switch Out of Control Saint of Me Too Tight Thief in the Night How Can I Stop Don't Stop Rough Justice Rain Fall Down Back of My Hand Oh No Not You Again
Can't believe no one has mentioned the incredible Thru And Thru. There's a 9 min or so outtake from Voodoo Stew that is incredibly spooky. Probably the most modern the Stones have sounded in since 71.
But Love Is Strong, Back Of My Hand, Rough Justice, and Out of Control are pretty darn good too.