You're making me introspect a bit Tom, that's good. I assume you are referring to music that is traditionally associated with accordions. Since starting to study accordion again I've listened to more strictly "accordion" music than I had in about the previous 20 years. Before that on rare occasions I would look up a video for a song like dark eyes or a tango because I wanted to hear it, and if there was a accordionist playing live somewhere I would hang around and enjoy the show. During that time I was occasionally playing accordion for myself, mostly my own songs and maybe practice a few Christmas songs around the holidays. Now that I'm studying my focus is on developing my skills on the instrument so I'm learning the regular tangos, waltzes, and polkas (and that's about the order in which I prefer them). I don't dislike polka music or anything, it goes great with beer and friends. I just have to be in a really specific mood to want to listen to it by myself. I also have slight concern about validating the common (at least where I live) misconception that polka is the ONLY music the accordion is suitable to play. I am happy to learn how to play tangos, waltzes and polkas to develop my skills and I plan to keep these songs available to play, it isn't my intention to be an expert in these styles. My goal with the accordion is to be able to play at a reasonable level of skill many of the styles of music I like. This will let me best utilize the instrument in my original compositions and allow me to go out with a single instrument and entertain people. I think I'm approaching the point where I can start trying to tackle some baroque pieces. I really like the sound of this but I have a suspicion the skill level required to play it will elude me.
The thing I like about indie music is that it has a very wide aesthetic, taking cues from a wide variety of existing styles of music. There are several bands in this genre that use accordions in various degrees (even though they are using them I think they could use them in a better way ;-) ). I wouldn't call this "accordion" music but a lot of it can be adapted to accordion. This is the kind of music I write mostly.
While I love hearing an accordion, by itself it can get tedious after a while and with some complimentary instruments can be more interesting. Personally I feel that waltzes are best suited for the accordion and if played reasonably well audiences also seem to react the same way. Tangos are good but so are foxtrots and rumbas as well as chachas. One of the main reasons that I invested in a Roland Fr8x was because I could make the accompaniment more interesting and sounding like it should for those various styles. As much as I like complimentary instruments it's difficult to find someone on the same schedule with whom you can play.
I cheat a little using music for the keyboard which consists of the lead and the complimentary chords. This also reduces the need to turn pages when using paper charts. Keyboard music also tends to have mostly contemporary music so it might help you to expand your repertoire.