In my 40s, but since others who didn't yet hit 60 offered great suggestions, I'll throw a few who embody my generation...
Beastie Boys, The Cure, De La Soul, Gang Starr, Guns N Roses, Metallica, Nirvana, NWA, Liz Phair, The Roots, Run DMC, The Smiths, A Tribe Called Quest, Weezer, Wu Tang Clan