I listen to a bit of everything. I grew up on country music. I don't care for a lot of the new country music though. Whatever it is I'm listening too, I want to understand what they are saying. A good beat is a must.
As far as the general question, I listen to just about anything.
I grew up in a very musically eclectic home. My dad liked bluegrass and classic country, and my mom liked R&B and soul.
I have five siblings, and they all had slightly different tastes. I always identify my siblings with their albums from when we were growing up. From oldest to closest to me (I'm the youngest):
1. Cat Stevens/Tea For The Tillerman
2. Johnny Rivers/Live At The Whiskey-A-Go-Go
3. Elton John/Captain Fantastic And The Brown Dirt Cowboy
4. Steve Miller Band/Greatest Hits
5. Fleetwood Mac/Rumors
Of course, everyone had a fair sprinkling of Beatles, Eagles, Neil Young, and Jackson Browne (it was the '70's).
From my own generation, I remember liking Tom Petty & The Heartbreakers very early on (still do), and I became very enamored of Appalachian music, and then the Celtic music that came before it. Still listen to a lot of that now.
As I became interested in guitar and studied that, I concentrated on a lot of acoustic guitar based artists, like Bert Jansch and Pentangle. Still listen to a lot of that as well.
I also like "weird" stuff like hardanger fiddle music from Norway, hurdy-gurdy playing, etc. One of my favorite recordings is from National Geographic (or some similar outfit), and involves the southeastern US phenomenon of hollering - a vocal practice used to communicate from field to farm, or mountain down to valley - akin to yodeling, but it doesn't sound like yodeling at all.