When it comes to art, I know what I like. But why do I like what I like? At the highest level, I would say that I prefer art that exhibits what Ayn Rand called joy and reason and meaning (see her description of Monadnock Valley in The Fountainhead). However, my understanding of that phrase is broader than Rand's. For me, 'joy' stands for art that is positive, constructive, pleasing to the senses, not only art that exhibits "man-worship" or a heroic sense of life; 'reason' stands for art that is intelligible, conceptual, open to understanding, not only art that upholds an explicitly rational view of man and the universe; 'meaning' stands for art that has something to say, that is interesting, that takes life seriously (or that takes fun seriously!), not only art that is explicitly philosophical. And my application of joy and reason and meaning is broader, as well. For example, Rand thought that Rachmaninoff's Second Piano Concerto and Tchaikovksy's First Piano Concerto are some of the highest artistic exemplars of joy and reason and meaning, but I find those values in a wide range of music that she did not like, such as Bach, the Beatles, and Duke Ellington. Another difference with Rand is that my artistic preferences tend toward small-scale, intimate works and forms, and away from the grand scale. For example, I prefer chamber music to concert music, poetry to novels, song to opera.
My favorite art-form is music, with poetry a close second (perhaps this is why I enjoy songwriting so much). Sculpture probably comes third -- I like the tactile dimension in addition to the visual -- but drawing and painting are high on my list, as well. I don't find myself especially attracted to stories, which is why fiction is not one of my great loves, although here I prefer plays to both novels and short stories, and have found myself liking drama more and more. I like architecture (when it is intended to be aesthetic) but I am woefully ignorant of dance. Probably my strangest characteristic is that I dislike movies or, to be more precise, the medium of film; while there are several movies I have enjoyed, overall I find the medium off-putting and disturbing in some elemental way.
In music I show a strong preference for melody, but I also like music that uses tone-colors and harmonies in interesting ways, for example the music of Duke Ellington. I guess I have what the jazz musicians call "big ears" -- I like all kinds of music, including "art" music from the Renaissance to present times, jazz (esp. Ellington), blues, rock (esp. Yes), reggae, bluegrass, and folk.
Most of the poetry that I like is metrical or at least highly rhythmical and, as befits my intellectual bent, somewhat philosophical as opposed to purely descriptive. I also take a great deal of pleasure in word-sounds and word-play, which is why I enjoy poetry (including some nonsense poetry) that uses rhyme, alliteration, and other effects of language.
The works of sculpture that I like are figurative and (generally) positive, though I like some works (such as the Adams Memorial by Augustus Saint-Gaudens) that are not exactly upbeat.
In the art of painting I tend to prefer works that are representational, that emphasize the play of light, and that use color in striking or original ways -- thus my love of Vermeer and Sorolla.
Fiction -- by which I mean novels, short stories, and plays -- is, as noted, not my favorite art-form. I think my tastes in fiction tend to be fairly conventional (interesting characters, happy endings, and all that) and to follow my ideological predilections (humanism, individualism, libertarianism, and so on). Although I used to read science fiction novels quite regularly, in the last few years I have nearly stopped reading novels. However, I have become much more enamored of drama (experienced both live in the theatre and by reading plays in the quiet of my home) and could even see trying my hand at playwriting sometime.
I like so few films that it's hard to generalize about my preferences and in any case they're probably quite idiosyncratic -- for example I refuse to watch movies with violence, I can't really handle movies with a great deal of suspense, and many of the movies I've enjoyed have been either animated films or in highly "nonrealistic" genres such as science fiction.