The subject is difficult, as indicated by a few who have admitted they are not sure their response makes sense. By that I think we mean we want to make sense but we are reaching out to define an understanding that in some ways approaches the indescribable.
Perhaps it is difficult because the answer to the question occurs on several levels at once. There is an inherent liking of music for some folks. We cannot help ourselves.
Some of us are those who would sing anything fun to sing when we were kids. I, for one, recall singing "100 Bottles of Beer on the Wall" over and over and over as our family traveled down Interstate 80 across the Bonneville Salt Flats in western Utah state. If you have not been there imagine driving down an arrow straight highway that shoots for about 50 miles across pure-white, salt encrusted soil, perfectly flat and stretching to the horizon in every direction. Then imagine you are 11 years old and stuck in the back seat. That setting has its own form of psycho-drama but add to that my incessant singing - I do not know how my parents survived.
Here is a description of the salt flats.
http://www.utah.com/playgrounds/bonneville_salt.htm
So that is one level of musical enjoyment - one that I still like - to absentmindedly allow a tune to fill my heart with simple joy.
As I got older and developed an ability to play though chords on the piano and guitar I found the joy of hearing different tones create new impressions. It is one thing to enjoy hearing someone else play and another to discover you can manipulate the notes yourself, even if you are playing the same thing. Cycle a diminished chord through its related major and minor keys and it can keep you busy all day, filled with wonder.
Now I am old enough to know my limitations - old enough to let the experts show me how it is done and to appreciate their art. This has multiple levels of its own: performance, composition and recording. I've experienced enough with recording to know it has its own musical artistry. Read about the placement of microphones in a large church to record the best sounds of a cathedral organ (in the organ forum) for an example. This last level touches on what has emerged as "home recording", much of which is available on this website. It serves an important purpose for those who can hear their compositions more broadly than a solo part on their chosen instrument. The reality is not everyone can access a symphony or chorus to give their work a larger expression.
Well fine. In the end I like music because if I want to rejoice or cry or lament or rock out, there is music that lets that expression become my own. It can be found by my keeping time to the beat of my heart, or a song on the radio as I drive down the freeway. It can be found when I am whistling as I wash my car, singing a lullaby as I tuck my kids into bed, or worshipping on Sunday. It has a universal appreciation across ages, eras and cultures. It brings healing to the soul more immediately than can other arts that require time for reflection. It can be found wherever I am. I do not need a venue or an ensemble or any materials at all. Not only can I create it with my own voice, but I can hear it in the waterfall, the rain, the crickets and frogs on a late summer's eve.
Hmmm, I think I like music a lot because it brings me joy.