R>H>M
Rhythm is just something that gets into my head and sticks (especially if it's in 5. I love the feel of five).
Harmony can make some amazing tension and really give a piece/song colour. Without harmony the music can be very grey.
Melody is very nice, but without the other two it is often uninteresting. It is the other two which give rise to the effect that the melody has.
I would list an exception as being when every or a majority of instruments in a piece are playing more melodic lines (including the bass instrument), but still, the various counterpoints still provide a very definite set of shifting harmonies which allow for the overall colourful complexity to be obtained.
Man, I sound like a pretentious moron.