Music parents like? Alright, I'll go.
My dad is pretty stuck in his ways, honestly. He'll tolerate some of the stuff I like, but anything too weird he dislikes. Clapton, Bryan Adams, The Beatles, Beach Boys, Fleetwood Mac, Springsteen, Andre Bocelli that kinda stuff, and not a whole lot else. He generally dislikes anything too heavy, although he likes the occasional Zepp song, and once told me he owned a Black Sabbath album, which I find a little hard to believe.
My mum's a little more open minded. She likes the same stuff, although she digs a little more weird and heavier stuff from the same era, ie Pink Floyd, Cream, Hendrix, etc. She's not really into anything too metal-oriented, but that's understandable. She's into folk pretty good, like Simon & Garfunkel, Dylan, Cat Power, even Nick Drake. She likes a good lot of the indie stuff I like, as well, but won't actively search it out. I've played Bon Iver, Fleet Foxes, The Shins, and I dunno what else and she's always enjoyed it, so long as it's not too freaky.
So yeah, my mom's a lot more open minded, although she's always been far more artsy in all respects than my dad, whereas he's more numbers and logic.