I probably could do this for a number of artists, but let's just go with Madonna for a moment. There are two of hers that I really like for some reason.
Song: Crazy For You (yeah, I said it)
Why I like it: As the old song says, blame it on my youth. Sure, the production is so '80s it hurts, and the lead vocal seems a bit lacking in assurance, but I like the melody and changes more than I do in most of her stuff, particularly that nice little winding melodic thing that goes to the repeat chorus at the end. Much more importantly, the background vocals make me think of The Association (Windy, Never My Love, Cherish), whom I loved when I was a young kid. The first vinyl LP I recall buying with my own money (saved up from allowance and mowing lawns) was The Association's Greatest Hits.
Song: Ray Of Light
Why I like it: Not quite sure, as this kind of thing is not really my bag and never has been. No cool changes, pretty repetitive in a couple ways. But the instrumental track is actually kicking--I guess that's William Orbit?--and Madonna does a surprisingly (to me) good job of riding the groove and sounding like she's on top of it and having a blast. Plus I like the vocal lift at "And I FEE-EEL."