"Just Like Heaven" by the Cure
I never saw the Cure live, but have very fond memories of watching a local band (The Angry Neighbors) perform an excellent cover of this song at a Springfield, IL bar in either 1989 or 1990. At the time, I was recording a demo tape for them in my basement studio and they also included a cover of my band the Beyond's song "Like This" in their set. As far as I know, that remains the sole cover version of a song I had a hand in writing!