I'm not fanatic about the Stones, but I'm a fan, and I've been surprised by their longevity and the quality of much of their work, even after 1971.
The Stones got started with a bang. Their early records were all worth hearing. The debut, England's Newest Hit Makers 1964, is an amazing first effort. The covers of American R&B are all solid, and there's even an early Jagger/Richards classic in Tell Me. Now! 1965 is the debut's equal with more great R&B covers, and Jagger/Richards' Heart of Stone and Off The Hook are solid. More great covers and even stronger Jagger/Richards efforts fill Out Of Our Heads 1965, with Satisfaction, The Last Time, Play With Fire and The Spider and the Fly showing off their quickly developing writing prowess. December's Children 1965 is a collection of songs not previously released in the US with a few US singles. No new recording sessions were done for the record, It is another fine blend of covers and originals (half of the songs). Get Off My Cloud, As Tears Go By, and I'm Free are standout originals, and although it was cobbled together for the US market, it is another worthy outing from the early Stones.
The Stones were treated similarly to the Beatles in that their US and UK records were not the same, even though many were released with the same title. The first five UK releases were turned into seven albums in the US, with the addition of singles and UK EPs.
Next up was Aftermath 1966, the first Rolling Stones release with only Jagger/Richards originals. It is highly regarded as a classic, and I'm not one to argue, but the US release is front-loaded with many of the best songs, kicking off with Paint It Black, Stupid Girl, Lady Jane, and Under My Thumb. Their songwriting is strong and the performances are excellent, with Brian Jones becoming more a multi-instrumentalist than merely a guitarist, and adding color and variety in the process. 1967 saw the release of Between The Buttons, another all-originals set, and while not quite as fine as Aftermath, it's very close, and more varied in both writing and performance. Brian Jones plays no less than twelve instruments in addition to guitar, and Jagger/Richards produce a varied set of strong tunes. While it is ostensibly a compilation, Flowers 1967, released in the US only, had three songs that had never been released, and two others had only appeared as singles in the US market. Although derided as a promotional ploy for the US market, it has plenty of good songs, and a few that were only available on this release at the time.
December 1967 brought Their Satanic Majesties Request, the first Rolling Stones record that received mixed-to-poor reviews. The record was their first self-produced effort, their only psychedelic release, as far from rhythm and blues as they would ever stray, and mostly a mess. She's A Rainbow and 2000 Light Years From Home save it from the junk bin, but it is their only early stinker.
Beggar's Banquet 1968 began the run of their four finest records, all produced by Jimmy Miller, and released between 1967 and 1972. A grand mix of rockers and blues, it is a classic from start to finish. With Sympathy For The Devil, Street Fighting Man, and Salt Of The Earth showing their mature songwriting and arranging, and the funky blues of Stray Cat Blues, it is just a fine record. It is also the first time that they adopt a country sound for some songs, a trend that will continue throughout this classic period and beyond.
Let It Bleed 1969 continues in a similar vein to Beggar's Banquet. Rockers, country and blues all show up in spades, and it is another Stones classic. The record has a darkness to both the music and lyrical themes that sets it apart from anything they did before it. Gimme Shelter, Let It Bleed, Live With Me, Midnight Rambler, and You Can't Always Get What You Want all rock hard, and Love In Vain and Country Honk show off their country blues to fine effect. Another one that rewards listening all the way through, just like it was 1969 again.
That brings us to Sticky Fingers 1971. With the full integration of Mick Taylor's guitar, and a near-perfect set of songs, it is the Stones' finest hour. Brown Sugar, Can't You Hear Me Knocking, Wild Horses, Bitch, You Gotta Move, and Dead Flowers are all stand-outs, and there isn't a song, or even a note, out of place. They have done much good work since this one, but they've never bettered it.
At this point I should mention Singles Collection: The London Years 1989, a compilation on 3 CDs or 4 LPs that contains all the singles and B sides from 1963 to 1971. There are a ton of Stones compilations, and a few really good ones, but this one is just the bomb. Quite a few lesser known B sides, and a great overview of the most interesting period for the band.
Which brings us to Exile On Main Street 1972. It is a shambles, and it is great. It is the most Kieth Richards of any Stones record. A friend recently derided Kieth's technique as primitive and sloppy (I know, shocking, right?). But that's at least partly true, and this record is the proof. And it is also a really fun sort of Mott The Hoople kind of mess. I love it, then I'm less crazy about it, but it is a singular record in the Stones catalog, and maybe anyone else's. Recommended tracks: Side 1, Side 2, Side 4, and more than half of Side 3.
I'm not so aligned with the more recent positive reassessments of Goat's Head Soup 1973. It was always a disappointment, and maybe the bar was too high after the four beforehand. It has good songs- Angie, Heartbreaker, Star Star- but the lesser songs sound like a band running on fumes and bubbles.
It's Only Rock and Roll 1974 was a mixed bag, but the high points got higher than Goat's Head Soup. Ain't Too Proud To Beg, Time Waits For No One, and the title track stand up to their best work. But this is going to be the way ahead for most Stones records to come. A few solid singles destined for the next compilation (they released more compilation albums than studio records), and a lot of mediocre other stuff.
I'll just shorten things up here and say that description applies to all of the following: Black And Blue 1976, Emotional Rescue 1980, Tatoo You 1981, Undercover 1983, Dirty Work 1986, Voodoo Lounge 1994, Bridges To Babylon 1997, and A Bigger Bang 2005. If your favorite is in there, that's fine, they all have a few tasty morsels, but limited moments of high quality rock and roll.
So what were the standouts since 1972? Some Girls 1978 qualifies as a really good one. When The Whip Comes Down, Beast Of Burden, Shattered, Miss You and the title track are hot, and they sound rowdy and young and full of themselves, which has always worked for the Stones. Steel Wheels 1989 was a solid return to form after a pretty awful decade. Even if the singles didn't outshine their past, the record as a whole held up quite well. And the featured ballads, Almost Hear You Sigh and Slipping Away, are both classics. Stripped 1995 is shockingly good at this point in their career. I'm not spending time with their plethora of mostly dull live records, but Stripped,
billed as live, has only 6 live tracks recorded in small venues, and 8 "live in the studio"
tracks. Jagger sounds particularly inspired, and the acoustic guitars
and mix of songs are a blast.
I don't quite know what to say about Blue & Lonesome 2016. It's all old blues songs rendered with respect and reverence. It's OK. Maybe you loved the early sixties R&B material and hear a resemblance. But it is not R&B, it's straight blues, and it just never grabbed me. While Kieth Richards and Ronnie Wood are good guitarists, they are not really blues players. Your mileage may vary.
There are a lot of compilations covering various periods, and most are pretty good. GRRR! 2012 is the most complete career overview, and does a good job if you want the hits and a few other standouts. It came in 2, 3, and 4 disc versions, with 2 missing too much, 4 a bit of overload, and 3 just right, Goldilocks.