My all time favorite of theirs is Between the Buttons because I grew up listening to my parents copy of it along with all their Stones 45s......Yesterdays Papers....oh yeah.
Even though it's not an album, The London Years is my favorite Stones cd/collection or whatever. It was the first cd I ever got in 5th or 6th grade.
Out of these I'll break the tie and vote for Beggars even though I love them all.