First choice
Godspeed you! Black Emperor - 'East Hastings'
As used in the opening scenes to 28 days later. Technically not a song since there are no lyrics and it is seriously cut short for the film but a great choice, fits the scene perfectly. Slowly builds as the film sets the scene of a London decimated by a plague and ultimately abandoned and left to the infected.
Second Choice
Guns n Roses - Welcome to the jungle
As used in Grosse Point Blank, not my favourite band but a very clever use of the song. the main character, Martin Blank, returns to his home town for a school reunion only to find his childhood home has been demolished and replaced by a convenience store. He is listening to the track on his car radio as he finds the store, as he walks in an easy listening/lift music version of the same track is playing in the store.