If, besides from ABBA, you're a stringent Madonna fan such as myself, you'll appreciate this video. It's a version of Like An Angel Passing Through My Room that Madonna recorded some time during the period 1998-2000. It would have ended up on the Ray Of Light or Music albums, had she chosen to release it.
Madonna's take on the song - in my case, at least - takes a little while to fully appreciate. It's quite different from ABBA's version, and Madonna's vocals are not quite as suited to the arrangement as the elegant solemnity of Frida's. However, it is still not a bad piece at all, and so kudos to Madonna for choosing to give her own interpretation to such a beautiful song.