I think the Rolling Stones are the biggest and best rock and roll band of all time, and I don't think it's particularly close.
The Beatles were more influential, but I listen to the Stones 10x more often.
Everyone's gonna list the monsters here - Paint it Black, Satisfaction, Sympathy for the Devil, Gimme Shelter, etc. There are no wrong answers. But for me, those tracks are ubiquitous. I hear them often enough that I don't need to seek them out, and their impact has been blunted by overexposure. Those songs are just so popular they no longer resonate in the way they used to.
My favorite Stones tracks right now are:
Rocks Off (the most underrated song in their catalogue. Starting Exile with this song, and then going into Rip This Joint told you right off the bat they're not fucking around. Shit, we could have a whole thread talking about Exile only)
She's a Rainbow
Shine a Light
Factory Girl
Angie
Dead Flowers
As is the case most of the time, my favorite songs are ballads written by rockers. It's probably why I love the Replacements so much...