1) Soft Cell's cover of Tainted Love which has already been mentioned is, in my humble opinion, far better than the Gloria Jones version.
2) Japan's cover of the Smokey Robinson & The Miracles' song Second That Emotion - something about David Sylvian's voice just puts more soul into it for me
And finally...
3). Alison Krauss & Union Station's completely different slant on the old Foundations song Baby, Now That I Found You. Again, just something about it makes me feel there is more 'heart' in their (Krauss's) interpretation of the song.