I actually ended up hating this song... a lot. Every once in a while I will listen to it, but I have to be in a very specific mood for it.
I normally stick with Fortress Around Your Heart, Perfect Love... Gone Wrong, Ghost Story, A Thousand Years, Fragile, Be Still My Beating Heart, and Never Coming Home. I listen to loads of his other songs too, but these are the ones that get the most playtime on my music player/iPod.
This song, like De Do Do Do, De Da Da Da Da or Everything She Does Is Magic, seems too popish or overplayed, like Roxanne, to me. It's a good song though, just something I have to really been in a mood for.
Wonder why you wound up hating this song... For some reason, it's always fresh sounding when I listen to it and the words speak volumes for my life and I think that's part of the affinity one has for a song.
Love many of the others you mentioned as well ~ Fortress Around Your Heart and Be Still My Beating Heart are other favorites. My favorite Police song is 'Spirits in the Material World'.