This is a category where I might have English bands ahead of my favorite American bands, but as far as American bands go, we can make cases for acts like Elvis Presley and the Beach Boys. Both would be excellent choices, but they haven't stood the test of time for creating new music. Tom Petty and Van Halen - sure. Both were/have been around a long time and made great music spanning decades. I would have Aerosmith and the Talking Heads on any list. Eagles, Allman Brothers, Metallica, Nirvana, Pearl Jam - they all deserve consideration. And of course, Bruce Springsteen. Bob Dylan (more of a solo act), Billy Joel, Santana. Jimi Hendrix, the list goes on.
But for me, the greatest American band has to be the Grateful Dead. They started out almost 50 years ago, having played thousands of concerts along the way to many millions of fans. They have the distinction of hosting the first concert with more than 100,000 ticketed fans (Englishtown Raceway), and drew over 600,000 to Watkins Glen (along with the Allman Brothers and the Band [Canadian]. This year, they just concluded another successful touring by selling out huge stadiums across the USA. At a minimum, the Dead are certainly the greatest touring band of all time.