Wow. So many to think of and choose from. Off the top of my head, and in no particular order, and cherry picking through their catalog for some: Frank Sinatra, Elvis Presley, Tom Petty and The Heartbreakers, The Allman Brothers Band, Louis Armstrong, Melody Gardot, Joni Mitchell, U2, Neil Young, The Band (original incarnation), Miles Davis, The Beatles and many others. A bit away from a more direct answer to the thread question, but my music listening is what it is, a mix of many things.
The Rolling Stones and the Beatles begat everything else I have ever enjoyed in the realm of rock and roll music. The Stones were my favorite, because I especially identified with the energy of their music, but I loved both bands from an early age. From there, I found Bowie, Pink Floyd, Led Zeppelin, Bruce Springsteen, and then as I hit my teenage years I got really into U2, Talking Heads, Lou Reed and Velvet Underground, Laurie Anderson, and from there I always looked for music whose energy moved me, whether it was the melodies, or grinding guitars, or superb lyrics.
In my 20s, I discovered that not all jazz was sleepy and boring-- There is some brilliant jazz out there. Cannonball Adderly woke me up first, then Grant Green, and then Miles' electric and funky improv material, then several others. Today I love Bill Frisell, Julian Lage, Mary Halvorson, Ralph Alessi and others!
But I still love Rock and Roll, and The Rolling Stones vibe lives on in bands I love like Wilco, Heartless Bastards and Kings of Leon! But also there are soooo many other interesting younger bands out there-- The idea that "there aren't any good bands/ artists these days" is just very, very untrue. You just have to look around.
Moral of the story: There's so much great music out there. I thank the Rolling Stones for keeping my standards high. :^)