"Fade into You" by Mazzy Star (1994)
Appeared in Angus (which, PS, is a terrible movie about a high school outcast learning self-confidence. It was almost unwatchable, and this is coming from someone who voluntarily sat through Lucas the other day) and the Gilmore Girls episode "Rory's Dance."
"Wild Horses" by The Sundays (1992)
Appeared in the Buffy the Vampire Slayer episode "The Prom," also known as the end of the glory days of Buffy.