I love real art, Rubens, Titian, Velazquez etc Great stuff but Picasso or Jackson Bollocks no thanks. Take a look at the Francis bacon load of crap on a theme of Damien Hurst. £120M Buy one get 2 free. Sorry for rant.
To be pedantic, "modern art" usually covers up to roughly the 1970s, art made beyond that it is generally called contemporary art.
I love modern art. Particularly German Expressionism, Futurism and Vorticism. I find it much more interesting than traditional art such as the artists Dave mentions, which while technically amazing do nothing for me emotionally.
Why the excluded middle? Generally I like quite a lot, but love only a few pieces or artists. If I'm visiting a new country and am in a major town then I usually look out the contemporary art gallery. It's the same for me with contemporary classical and electroacoustic music.
I know very little about art and think a great deal of the grandeur around it is pretence, however that could be because I know nothing.
If I like a piece I like it, regardless of whether it is considered "great" for whatever reason or if it is worth £10 or £10m (worth is only what someone is prepared to pay and does not mean it is good to look at).