Well, The Replacements were one of those bands, back in the day. One of the bands that was well-known enough to get signed to a bigger label, but never really explode, so people heard about them, but could feel like they were still underground, still theirs, even though big alterna it-girls like Winona Ryder were talking about them in magazine interviews. The fact that she liked alternative music only made it that much cooler, in fact.
Their sound morphed over the years, too, going from sloppy garage punk to something a bit closer to mainstream, bringing in other influences that mellowed them out a bit and made them easier to adopt more widely, while still keeping their punk roots. By the time of their last album, the one I pretty much wore out, they sounded a lot like they did on Fallon the other night. Want to know what this sounded like? Check out their appearance, and below that, their final album, All Shook Down.