Undoubtedly my favourite band of all time and reading through some of the great songs already posted nearly brought a smile on an otherwise boring typical work day
I always think with the Stones, it's funny how many people "love" them but aren't very aware of their albums and the sheer size of their backlog. I think most wouldn't have heard of the majority of my favourites... so when you meet and talk to another Stones-obsessed person, it really strikes a chord (pardon the pun). And indeed I started the same way, greatest hit style albums to get into them... and then delving into all their album work as I just couldn't get enough!
Anyway enough slavering. To answer the question:
Let it Loose. My favourite song ever. Period.
After that, I'm like others in that I would struggle to pick an order. Some honourable mentions however (at this moment in time) for:
Can't you hear me knocking (THIS is the intro for me)
Far away eyes
Just my imagination
Memo from turner
Shine a light
Worried about you
Ok I'll stop. What a band. Won't ever be beaten.