That, I think, is one of the elements to music that I enjoy. Sure, I like a pretty melody, I like soothing strings, but for the most part, the music I really get into really challenges the listener in some way.
Film music is a perfect example. While the standard film score has many elements similar to classical and romantic music (and sometimes modern music), it is something all its own. The language of a film score is often dictated by an aspect external to the music itself, such as the pacing of a scene, context of the film's overarching themes, the dramatic requirements of the film, and so on. There is a craft at work in film music that informs the art, something that is very different from absolute music (although it has this in common with opera and ballet).
I also listen to a lot of classic rock, almost entirely from the post-single, album-dominated 60s and 70s. This is sort of an anomaly in my musical tastes, as I tend more towards the difficult elements of absolute music and film music.
Much of what I listen to in the classic rock genre is, of course, pop art, but I feel that the cultural revolution that was occurring at the time period that Jimi Hendrix, Led Zeppelin, CSNY and so on meant that the music had a strong counter-cultural element to it that makes it still sound fresh today, even if many of the synthesizer effects have dated (the VCS3 appearing in Pink Floyd's "Any Colour You Like" on Dark Side of the Moon and the Doors' "When the Music's Over" on Strange Days sound rather rickety by today's standards, although I wouldn't trade either song for a redone version for anything).
This was music that was discovering itself, which is apparent in Hendrix's "1983... A Merman I Should Turn To Be" on Electric Ladyland; it is also noticeable in the large amount of jam-produced music that appears on albums of this era ("Voodoo Chile" on the previously mentioned Hendrix record, "Cowboy Movie" off of David Crosby's phenomenal If I Could Only Remember My Name...).
I still haven't figured it out yet, but for some reason it seems to me that the reason why this era contains so much fascination for me is that there is so much in the music to hear. Take any Led Zeppelin album, for example, and you will find that there are any number of songs to stimulate the listener from ballads to hard rock. It is the enthusiasm of the band for the songs they write and the music that they play that comes across on the albums. In this way, it is similar to jazz, in which the performance element is as important (if not more so) than the composition.
Listen to music.