there are way more - those are just the ones I can remember 100%
'Jonathan' here is Cillian Murphy's character

- "1979"
   Written and Performed by The Smashing Pumpkins
  
:: read the lyrics ::
  
scene: opening credits while Jonathan is riding with his bike to his Dad's funeral

- "La Valse"
   Written by Maurice Ravel
  
scene: Jonathan drives off the cliff

- "Rudolph the red-nosed reindeer"
  
scene: Jonathan enters the mental institution

- "The Entertainer"
   Written by Scott Joplin
   Performed by John Carney
  
scene: during Jonathan's one-on-one therapy sessions with Dr. Figure 

- "Catch the Sun"
   Written and Performed by Doves
   :: read the lyrics :: check out the official doves website ::
  
scene: the patients are bowling

- "Please forgive me"
   Written and Performed by David Gray
  
:: read the lyrics ::
  
scene: end credits

- "The end of nowhere"
   Written and Performed by John Carney
  
scene: end credits