I actually listen to much of what they listened to. I’m a fan of the easy listening station and the “oldies” station, so I listen to a lot of 60s-80s pop and rock, which is exactly what my parents listen to. I mean, they play some newer stuff, too, but nothing that my parents would have a cow about.
My mom and dad are divorced and they have different tastes in music so I can’t really give a good answer. About the only things my mom and I agree on are most of the huge non-heavy-metal classic rock artists (beatles, eagles, etc.) My dad, otoh, is too into many different styles of current music for my tastes (he’s 60, I’m 36). While this has its good side, in that he doesn’t mind like my mom would when I play new rock music when he’s in the car, it also means that occasionally he will listen to soul-pop with me in the car :eek:
But sometimes my mom can surprise me. You see, she likes classic rock because she grew up with it and so is familiar with the songs. Whenever I play even a classic rock song from that era that she doesn’t know, she never gets into it because she had never been exposed to it. So when I was playing Rock Band when she was in the house and Alabama Getaway came on, I wanted to have her take a listen because it was right up her alley, theoretically (she likes country/classic-rock-ish stuff.) But I decided not to because chances are she wouldn’t like it because she had never heard it even though it’s around 30 years old.
Then she walks by and says “This is sort of good. Who is this?”
Me : “Grateful dead. It does have a nice sound but I didn’t think you’d like it because you’d never heard it before”. :smack:
There was an awful lot of bluegrass and gospel music in my house growing up. I’m no fan of gospel–I think I’d listen to country first–but I have developed an appreciation for bluegrass.
My love for quarky pop rock (Regina Spektor, Feist) and rock-rock (Aerosmith, Velvet Revolver) was about as appreciated by my parents as my appreciation for their music. However, I do love classical choral pieces, so we called it a truce with those.
Pop music (BareNaked Ladies) was less offensive to them, BTW.
My parents are deceased now, but they were definitely from the pre rock n’ roll era when it came to music. My mom preferred a lot of big-band and oldies music (read: Frank Sinatra, Dean Martin, and other vocalists of the era). My dad mostly listened to sports talk radio in the car. Or whatever baseball game/football game/basketball game he could tune in to. I grew up on the Rolling Stones, Elton John, BTO, etc.
They didn’t detest rock music. But they preferred I didn’t crank the volume too high. As long it it wasn’t noisy, they didn’t care what I listened to. This was in the days before the personal stereo cassette player, so I didn’t have too many other options.
My parents listened to olde timey country music (Hank Snow, Wilf Carter, Marty Snow, that stuff). I listen to everything but country (although I do listen to the occasional country song - I have “Sin City” by Dwight Yoakam and k. d. lang playing on iTunes at the moment). There is very little overlap between our musical tastes. Fair’s fair, though - my parents forced me to listen to country for the first 18 years of my life, now I’m forcing my mom to listen to rock/pop for the rest of her life. 
We share playlists frequently, but let me clarify… they like “my” music if it’s stuff they already listen to (i.e. most 70s/80s rock). Occasionally I will find that my mother likes some random artist I’m listening to, mostly female singers and some jazz, but besides that, I’m on my own. Fortunately for me, I have pretty eclectic tastes and can usually find something in common with everyone. And even more fortunate for me…I live alone, so I rarely have to try to please anyone else.