I may be alone here, but I generally personally enjoy a lot of modern art more than more classical art. I'm not going to try to argue that one is better than the other, and I certainly do see modern pieces I don't enjoy, and more "classic" pieces that I absolutely love, but as a rule I enjoy and feel like I get more out of visits to modern art galleries than I do when I visit more traditional galleries. But that's just me. One big exception here, I do tend to really love older Asian art.
I am learning to enjoy more traditional art more, especially a lot of the dutch painters, (my fiance was an art history major and wrote her honors thesis on a few Dutch paintings, so she's been teaching me a lot) but at the same time I feel like I've recently come to appreciate a lot of more modern pieces too (she also enjoys, and knows a fair amount about modern art too), so... yeah, honestly I feel like as i get older, pay more attention to it, and learn more about it I'm enjoying "art" in general more, but I still generally enjoy visiting the East Wing of the National Gallery of Art here in DC, more than the West (East is the modern side, though it's also the part with the biggest exhibition space, so sometimes more traditional things are over there too, just this weekend my fiance and I visited the excellent Pompeii exhibit, which was over in the East Wing exhibit space, if any of you are anywhere near the DC area between now and March 22nd I would highly suggest a visit. Or if you're near Los Angeles between May 3 and October 4th of 2009, hit it up there at the Los Angeles County Museum of Art!)