R.E.M. - 'So. Central Rain' (1983)
To most people outside of Athens, Georgia and the college rock scene in the early Eighties, R.E.M. were a largely unknown band. But they did have enough buzz to earn a Letterman slot on October 6th, 1983, playing an early version of "So. Central Rain (I'm Sorry)" off their sophomore album Reckoning — which wouldn't actually hit shelves for another seven months. It was the band's first time playing on network television, and it played a huge role in helping them reach a wider audience.