The Rolling Stones are the greatest rock band in the history of music. That’s it. Why? Here’s just five little reasons why…
Note: A lot of these clips won’t play on mobile devices. Sorry.
5. “(I Can’t Get No) Satisfaction” (1965)
It was their first #1 in the US and a standard at nearly every concert they’ve played since then. They’ve made it something of a show starter, at times.
4. “Paint It, Black” (1966)
From their album Aftermath, this song never fails to amaze.
3. “Sympathy For The Devil” (1968)
A song about the devil, part of their album Beggar’s Banquet (one of their best).
2. “Sister Morphine” (1971)
Written by Keith Richards, Mick Jagger, and Marianne Faithful, it was released by Faithfull a couple of years before it was part of the Stones’ legendary album Sticky Fingers (my favorite, if we’re picking).
1. “Gimme Shelter” (1969)
In 1969 the Beatles were breaking up. The spent part of their spring and summer recording their final album, Abbey Road. At about the same time, The Rolling Stones are in the studio making Let It Bleed. What a year for masterpieces. “Gimme Shelter” is the first track from that album.
Any list of songs by the Rolling Stones is selective. There’s no way to pick 5 songs, even 10, that represent the breadth of their work or that accurately portray their influence in popular music. So go listen to more!
LATINO LIKE ME 
Great picks, all … they are so good, I might do my own list that had five different songs, while still thinking your five belonged. (Truth is, I’d probably duplicate your list in many ways, and I’d also probably put “Gimme Shelter” at the top.) It interests me that most people who took on the challenge of picking the top five Stones songs would not go past Exile … that makes them seem like some novelty act from the olden days, but who else can we name who made 12 albums before they issued a dud (ok, some people think Satanic Majesties Request is a dud, although I’m not one of them). Most acts retire before they’ve made 12 albums, much less 12 great albums. (Meanwhile, I’d try to find room for “Rip This Joint”.)
“They” meaning “The Rolling Stones”, as in “The Rolling Stones are do good, we could pick ten songs … which is a point you already made :-).
Wow, I need to be able to edit my replies. “are do good” is “are so good”. I’m done now.
I’d love to see your list. Listening to them a lot over these past few months, and trying on albums that I normally cherry pick from, I was just amazed and how revolutionary they sound even now. It’s like 40 years later and they still sound fresh and new. And then the breadth! Like, the make songs that are so influential to so many others performers from so many genres. Lately I think Keith Richards might be the most underrated musical genius in popular music.
This really is impossible. I’ll do one per album through Exile … then I can pare it down more.
First album: “Tell Me”
12×5/#2: “Time Is on My Side”
#2/Now: “Down the Road Apiece”
Out of Our Heads: “Satisfaction”
December’s Children: “Get Off My Cloud” (or “She Said Yeah”)
Aftermath US: “Paint It Black”; UK: “Goin’ Home”
Between the Buttons: “Something Happened to Me Yesterday”
Their Satanic Majesties Request: “2000 Light Years from Home”
Beggar’s Banquet: “Sympathy for the Devil”
Let It Bleed: “Gimme Shelter”
Sticky Fingers: “Can’t You Hear Me Knocking”
Exile on Main Street: “Rip This Joint” (or “Tumbling Dice,” or “Stop Breaking Down”)
Honorable Mention: “Memo from Turner”
So, if I use the above as a template, the five songs would probably be Satisfaction, Sympathy, Gimme Shelter, Rip This Joint, and …. Tumbling Dice?