Great replies everyone! It's so interesting to see such a variety of responses. This is kind of what I was figuring. Everyone seems to listen or pay attention to or value different aspects of music. I guess that's what keeps music constantly evolving and allows for such a variety of genres/artists to co-exist...
You know that neurological study on the human brain on the right side controlling creativity and abstract concepts while the left deals with logic and maths.
Aparently the right-brainers are more in touch with a rhythm aspect of music while left-brainers are more in touch with the melody of music.
...and I would like to add that there is some music that doesn't even have melody at all, ambient music, free jazz and musique concrete, can do without melody. Rhythm (whether planned or random) is still a part of all musical styles...although other aspects are also important.