This is deeply embarrassing, but my favorite has always been Liza Minnelli's "Losing My Mind" (which is a version of the song from Sondheim's musical Follies) :
Shirley Bassey has a nice version of the above as well.
And I equally love New Order's Bizarre Love Triangle (but I love
everything New Order) in part because it was in one of my favorite 80s movies as a teenager:
In the 90s, there was a cover by Frente! that was
surprisingly lovely.
And this one, which is tied with Enola Gay; I can't possibly choose!
And I can't leave out Kate Bush! (though my true favorite of hers, Waking the Witch, is one I probably could not classify as pop)
In terms of modern pop.. I love Florence Welch, Prince,
Sleigh Bells,
Grimes, all of the angsty 90s indie-pop groups...And
St. Vincent,
Janelle Monae,
Stars,
Ladyhawke, etc.
OFFICIALLY, though, I think this is my favorite of the past 25 years: