I think a lot of times, these bands push some boundary or other that most casual listeners aren't aware of, so what they hear are songs that sound a little strange, rather than songs that are doing something unique. But then members of a band, being more aware of all the things that are easier and harder to do, musically, listen to these same songs and realize that something was happening there. Inspired, they take these strange sounds and refine them in a way that is more listenable to more people.
One band that I was thinking about this morning that I think falls into this category, is Wire. They've been making music since the late 70s. Their first concert, apparently, was the first time some of the band members had played their instruments. It didn't go well. But they stuck together and learned to play music together as a band. They've been through some crazy incarnations over the years, and are still producing music now. Here's a selection of my favorites:
'Strange' from their first album Pink Flag, later covered by R.E.M.:
'The Other Window' from Chairs Missing:
'Ahead' from the Ideal Copy, their fourth studio album. I love this song:
They just released a new album earlier this year, so I haven't had a chance to really listen to it yet, but don't let that stop you from tracking it down and giving it a shot. It's self-titled.