I'm terrible at knowing what song is what, but I'll try. The songs I remember are ones I can hear later and still feel the emotions of the scene they are from. I few of my favorites, Weapon and Lover's Spit have already been mentioned.
I can't talk about music and QAF without mentioning Save the Last Dance for Me. Such an incredible moment between Brian and Justin driven by the music. Any time I hear that song I stop what I am doing and remember how they looked dancing together. I've actually stopped talking midsentence.
It's no secret that I adore the final scene of 202. It's an incredible moment of healing and reaching out by Brian and Justin. Svefri-g-englar by Sigur Ros captures all of that perfectly. There really are no words to describe what is happening between them so a song that is about sound and emotion is the only choice.
I can't wait to see other people's answer so I can remember all the wonderful songs I can't think of.