Using Hazel's criteria of not including songs written for the show.

OK... I'll have to admit that I had to do some research here. I generally liked the music on Buffy in a kids with guitars way but most of it was pretty forgettable.

I remembered The Breeders being on... but it wasn't Pod Breeders, or even Last Splash Breeders it was Title Tk Breeders. I also remembered The Sundays being played but couldn't remember what or when - turns out it was a cover of The Rolling Stones' Wild Horses which I've probably only ever heard on the two occasions I've watched... The Prom - ugh - that bloody umbrella - shudder...

Luckily I found this site which helped me find a few great songs that I don't remember so Favourite Song Used In An Episode is...

Going to Hell by The Brian Jonestown Massacre as used (apparently) in the episode Faith, Hope and Trick...

Honourable mention to Yo La Tengo who under almost any other circumstances would have walked away with the prize... but Going to Hell suits Buffy so much better than Tears Are in Your Eyes. Teenage FBI by Guided by Voices is on a Buffy album but never turned up on the show (weird)