I was going to start my own thread like this but I'll just bring this one back from the dead instead.
Originally made a hit by The Marvelettes in 1966, Massive Attack's cover has an incredible sultry and slightly dirty sound that this song deserves.
Blondie's "Call Me" covered by In This Moment. The original is good but the hard rock sound and Maria Brink's vocals on this are amazing. Brink turning the sexy up to 11 doesn't hurt either.
I know the Depeche Mode fans will hate me for this one but I do like Lacuna Coil's cover of "Enjoy The Silence" Better than the original.
I was saving the best for last. Most if not every other cover of The Cure's, "Just Like Heaven" that I have heard is as fast or faster than the original, this version, done as a demo by the group Deadsy, is slowed down significantly and I personally think that the bass heavy, distorted sound, and reduced speed really fit the song well and make for the most unique cover of this song I have ever heard.