Not nearly enough people, in my book.
Look at it this way: there are drawing classes available to children and adults of every skill level, from beginning to student to professional. Everybody knows that drawing is a skill that most people can become at least somewhat good at; that drawing can be a source of continuing pleasure throughout life; that you can start at one level and progress as you learn more about your tools and your eye.
I'd like to see classical composition taught the same way as drawing: as a craft, or as a learnable skill. Instead, composing is surrounding by a golden aura of genius and prodigiousness, the legacy of a 19th century world view and, perhaps, those youthful composers Mozart and Mendelssohn. Either you're a brilliantly talented genius or you're nothing - how easy it is to forget that Leopold Mozart raised his son with music lessons from an early age, thus nurturing the inborn potential the child had. There are middle ways! As you work with music, you learn how to structure a piece, how to balance an ensemble, how to write a melody, how to compose for different instruments. All you have to do to realize the truth of this is to look at how far Verdi and Wagner came from their first to their last works.
Certainly pop and rock have figured this out; look at the thousands of kids playing guitar or bass, many of whom taught themselves to play, many of whom go on to start bands in their garages or basements. If we can change our attitudes about the nature of composition and start teaching it as a skill that can be learned and hones over time, we will have more composers; we will have more listeners who listen with skill; we will have more people playing instruments alone or together.
Speaking more personally, I never thought of myself as someone who might learn how to compose until about a year or so ago, when it dawned on me that I'd heard enough music and looked at enough scores that I could put together, on the one hand, a pastiche of a Donizetti aria, and, on the other hand, an original vocal trio, with orchestra, in a loosely Expressionist style. I haven't done either and probably won't (time, etc.), but it was quite a shock to me to realize I could.
(Elaine Fine and I have had an interesting email discussion of this topic, and I hope she'll post some of her thoughts as well.)