I heard the acoustic version of Taylor's State of Grace at a yogurt place. Once, a couple years ago, while driving in my car, I heard a promo for a Taylor related contest on the big local radio station here. The music in the background sounded familiar, but I couldn't immediately place it. After a couple seconds it hit me: it was Permanent Marker, a unreleased song that was a late cut from her debut album.
Back at the end of 2006, when Justin was huge with FutureSex/LoveSounds, the local pop station played his unreleased song "If I" late one night.
Not my fave, but I remember turning to a Music Choice channel and they were playing Justin Timberlake with what was being called "Magic" at the time it was leaked. It was the demo of "Love Sex Magic"... I remember everyone thought this was his comeback song...