Q:

Why do we like music?

Music is, of course, just a sequence of sounds. Sounds are vibrations in the air, which our ears detect. So why do we find certain sequences of sounds to be appealing? What makes us want to hear these sounds (turn on a radio, for example), or make these sounds on our own (sing/play an instrument)?
Heck, why do we even move our body strangely when we hear certain music (dancing)?

A:

According to the article Why do we love music?, "No one knows why we love music, or what function, if any, it serves."
Of course, that article was published in 2013, so it's possible someone has found an answer since then. ;)
Some have argued that music is merely an evolutionary byproduct that serves no really important purpose. (Type "auditory cheesecake" into Google.) In a similar vein, one might speculate that music did serve an important purpose at one time (e.g. a mating ritual).
In this spirit, we might ask how one defines music and then ask if we humans are the only species that makes music. When we hear frogs croaking or crickets chirping, are they merely communicating, or are they making music - or are they doing both at the same time?
Though your question focuses on music people listen to, a similar question could be asked about dance. Except I think music is more universally popular than dance, which doesn't interest everyone.
In summary, I haven't really answered your question - which probably can't be answered with any accuracy at this time. But there are actually lots of references on the Internet that offer clues to the puzzle. I suspect there's some overlap between the love of music and the love of poetry, painting, etc.
I just discovered an interesting term - evolutionary musicology - along with another theory to explain music's popularity: It may simply be a welcome break from silence, which may be associated with danger.

Yikes, I know I'm doing a lot of rambling, but here's another thought:
Some researchers believe music served as a sort of group bonding tool. In other words, a particular tribe might have produced a certain kind of music that helped unite members of that tribe. In other words, music could be a form of symbolism, similar to flags.
As a huge fan of Latin music, I've come to appreciate the association between specific genres and their places of origin. For example, flamenco is a product of Spain, while cha-cha-cha and mambo are forever linked with Cuba. There's a fierce debate about the origins of salsa, which was officially born in New York City but which is clearly derived from mambo.
No one can deny that country music sucks. Yet I love a lot of country music, which I was exposed to when I was growing up in rural West Dakota.
What I'm trying to say is that music probably helps us identify with a particular group and connect with our roots.
P.S. It's worth noting that other species do indeed enjoy music. Check out the article What type of music do pets like?

