My family is eclectic.The only music we will not listen too is rap.Don't get me wrong,I used to love the older stuff but everything nowadays is about killing cops,drugs or abusing women.My favorite classical composer is definitely Mozart.
I will listen to just about any kind of music, except progressive jazz, hip hop, rap, etc. I grew up with "hillbilly" music, but when my wife and I started dating in the 50s, she refused to listen to "hillbilly" and I refused to listen to classical, so we settled on the rock and roll that was becoming so popular then. My wife being a piano teacher for 40 years, gradually acclimated me to the pleasures of Classical Music. I particularly love the Romantid period. Also like SOME opera - Love Puccini's "Madama Butterfly".
I like classical, though I never really listen to it normally. I can listen to just about anything except for reggae, bluegrass and maybe a few other things. Personally I prefer rock, classic rock, and have really taken a liking to some "electronic music"/techno. I've found electronic music to be incredibly cool in that there is such a wide variety and many times you can find elements of a wide variety of other music types mixed in such as classical, jazz, blues, etc.
I listen to classical music a lot, mostly via XM Satellite, but also through two local FM stations. El Paso also has a symphony orchestra, but I'm ashamed to say I haven't attended a live concert in the four years I've lived here.
I enjoy music from the 18th, 19th and 20th Century; symphonies, concertos, string ensembles, soloists & choral works.
To paraphrase Will Rogers, "I've mever heard a composer I didn't like".