founded in the 1960s: The Beatles, The Yardbirds, Jefferson Airplane, Simon & Garfunkel, Chocolate Watch Band, The Doors, Jimi Hendrix, Led Zeppelin
founded in the 1970s: Roxy Music, Siouxsie and the Banshees, Ultravox, Blondie, The B-52s, Television, Gary Numan and Tubeway Army, The Ramones, Rush, Tom Petty & the Heartbreakers
founded in the 1980s: Depeche Mode, Duran Duran, Simple Minds, R.E.M., Eurythmics, The Smiths, Red Hot Chili Peppers, Sonic Youth, The Cure, The Pixies, Metallica, Nirvana
founded in the 1990s: Smashing Pumpkins, Garbage, Dubstar, The Cardigans, The Verve, Oasis, Orbital, Chemical Brothers, P. J. Harvey, Curve, Cat Power, Korn, Live, Linkin Park
founded in the 2000s: Metric, Broken Social Scene, Let's Go Sailing, Minipop, Los Camposinos!, Minus the Bear, Silversun Pickups, The Knife, Rilo Kiley, MGMT, Tegan & Sara, Interpol
My top three favorite for each are in bold and my favorite of these is underlined. But I am sure there are some big omissions that I've left out.