I divide the endless career of the Rolling Stones into 3 phases:
1) the early singles
2) "Beggar's Banquet" and "Let It Bleed"
3) everything else since
I enjoyed many of the early singles. We could all watch as the band was being born and growing up. Early experimentation with sounds like the fuzz on "Satisfaction", the Sitar on "Paint it Black", the feedback on "Have You Seen Your Mother, Baby (Standing in the Shadow)" showed a group of musicians willing to take chances. The writing was solid pop/blues. It was fun stuff and I couldn't wait for the next single to come out.
But "Beggar's Banquet" and "Let It Bleed" were near-perfect albums. The boys had matured, but they hadn't lost their edge. These were less bluesy than their earliest albums, and far more focussed. Surprisingly, these were produced during their most turbulent years emotionally, and featured three different rhythm guitarists: Founding father Brian Jones (who died durinig the recording), Mick Taylor (who stayed only briefly), and Ron Wood (who helped form the foundation of the newly reborn band).
The third phase, still going on today, is for me the least compelling. The single bright spot, when they ALMOST returned to their earlier form, was "Exile on Main Street". But even that doesn't stand up compared to these 2 classics from their middle period.