Stones.
Fine, so their most recent tune that I like as much as their older stuff is Undercover of the Night or Waiting on a Friend and they're from the 80's (not that Ringo, McCartney or Harrison did anything as good as their seminal work either), but what great tunes they had during the 60's and 70's.
Paint it Black, Sympathy for the Devil, Brown Sugar, Jumpin' Jack Flash, Mother's Little Helper, Only Rock'n'Roll, Street Fightin' Man, Little Red Rooster, Under my thumb, Satisfaction, Honky Tonk Women, Start me up, etc. All brilliant and timeless.
The Beatles are great too though. I especially like Sgt. Pepper's, the White Album, The Magical Mystery Tour, and Revolver myself.
Led Zeppelin, Van Morrison, The Kinks, The Who, and Velvet Underground deserve a mention too as great rock pioneers of the 60's and 70's.
If it breaks, you get to keep both pieces.