I hate picking "favorites"--with me anyway, my "favorite" depends on my mood.
Jimi Hendrix--perhaps the most creative merger of improvised blues and rock ever.
Carlos Santana--the father of "world beat"--fused Latin, Caribbean, and African, with American guitar rock in different combinations to create beautiful compositions.
The Beatles--The greatest POP band ever, and they went beyond pop, too.
Steely Dan--I've recently really began appreciating their talent and genius. They were perfectionists in the studio, doing take after take until they got it exactly right--and it shows. If you like impeccable horn and sax arrangements, check 'em out! Particularly the later albums.
Kansas--Symphony-quality compositions and spiritual (Native American and Christian allusions) lyrics.
Yes--Another band of symphonic-rock perfectionists.
Bob Dylan--Probably the most clever lyricist in rock. I generally listen to him for that reason alone, as musically he wasn't all that spectacular.
As for the Stones, I like them generally, but I can't say I get all excited about them. I saw them live in 1990 too (in Cleveland), and they SUCKED live--$60 for a ticket way up in the back seats of the stadium (that was a LOT of money for a concert back then), and they sounded like they were all drunk off their asses, and going through the motions half-heartedly. Disappointing, and I'm sure that clouded my view of them further....