Future Islands - 'Seasons (Waiting On You)' (2014)
These days, bands don't have huge breakthrough on moments on television like they did in the pre-Internet era; there's just so many ways for people to experience new music now. But occasionally a TV performance is so electrifying that it creates a viral sensation, and that's exactly what happened when the synthpop band Future Islands went on Letterman. Frontman Samuel T. Herring poured so much passion and energy into his vocal delivery (and unique dance moves) that nobody could possibly ignore it. "How about that!" Letterman said. "I'll take all of that you got. That was wonderful!" The world agreed — nearly four million views on YouTube, the appearance turned out to be a career-defining moment for the band.