New Moon songs in order of appearance in movie

So there is both a list of just the soundtrack songs as well as the soundtrack mixed with the score. Here you go!

1. New Moon – Alexandre Desplat.
2. Bella Dreams – Alexandre Desplat.
3. Monsters – Hurricane Bells.
4. Romeo & Juliet – Alexandre Desplat.
5. Volturi Waltz – Alexandre Desplat.
6. The Violet Hour – Sea Wolf.
7. Blood Sample – Alexandre Desplat.
8. Wandrers Nachitlied II, Op. 96, No. 3, D. 768 – Ulf Bastlein (iTunes bonus track).
9. Satellite Heart – Anya Marina.
10. Rosyln – Bon Iver & St. Vincent.
11. Edward Leaves – Alexandre Desplat.
12. Possibility – Lykke Li.
13. I Belong to You (New Moon Remix) – Muse.
14. Friends – Band of Skulls.
15. All I Believe (iTunes Bonus Track) – The Magic Numbers & Amadou & Mariam.
16. Shooting the Moon – Ok Go.
17. Werewolves – Alexandre Desplat.
18. Solar Midnite – Lupe Fiasco (iTunes Bonus Track)
19. I Need You – Alexandre Desplat.
20. Break Up -Alexandre Desplat.
21. Memories of Edward – Alexandre Desplat.
22. Wolves vs. Vampire Alexandre Desplat.
23. Victoria -Alexandre Desplat.
24. Almost a Kiss – Alexandre Desplat.
25. Done All Wrong  – Black Rebel Motorcycle Club.
26. Hearing Damage – Thom Yorke.
27. Adrenaline – Alexandre Desplat.
28. Slow Life (With Victoria Legrand) – Grizzly Bear.
29. Dreamcatcher – Alexandre Desplat.
30. To Volterra – Alexandre Desplat.
31. You’re Alive – Alexandre Desplat.
32. The Volturi – Alexandre Desplat.
33. Die Fledermaus – Duettino : Ach, Ich Darf Nicht Hin Zu Dir – APM Orchestra. (iTunes Bonus track)
34. The Cullens – Alexandre Desplat.
35. No Sound But the Wind – Editors.
36. Marry Me, Bella – Alexandre Desplat.
37. Full Moon – Alexandre Desplat.
38. A White Demon Love Song – The Killers.
39. Meet Me on the Equinox – Death Cab for Cutie.

SPOILERS if you are avoiding for some reason and have not seen it yet

1. New Moon – Alexandre Desplat.  Opening credits
2. Bella Dreams – Alexandre Desplat. Bella, Gran and Edward in the meadow.
3. Monsters – Hurricane Bells. Bella driving to school on birthday and Edward walking through school parking lot.
4. Romeo & Juliet – Alexandre Desplat. Edward and Bella in English class, discussing vampire suicide.
5. Volturi Waltz – Alexandre Desplat. Edward explaining the Volturi to Bella. Aro kills bad vamp.
6. The Violet Hour – Sea Wolf. Bella’s birthday party.
7. Blood Sample – Alexandre Desplat. Paper cut fight between Jasper and Edward.
8. Wandrers Nachitlied II, Op. 96, No. 3, D. 768 – Ulf Bastlein (iTunes bonus). Carlisle is stitching up Bella
9. Satellite Heart – Anya Marina. Edward taking Bella home after party in her truck, played on the radio
   
10. Rosyln – Bon Iver & St. Vincent. Bella at school without Edward and Edward telling Bella they need to "take a walk"
    
11. Edward Leaves – Alexandre Desplat. Edward dumping Bella in the woods.
12. Possibility – Lykke Li. Months passing for Bella.
13. I Belong to You (New Moon Remix) – Muse.  Bella and Jessica on Girls Night Out.
14. Friends – Band of Skulls. Bella on stranger's motorcycle
    
15. All I Believe (iTunes Bonus Track) – The Magic Numbers & Amadou & Mariam. Bella and Jake fixing motorcycles. It is the song playing that Bella turns off when she states she no longer likes music
    
16. Shooting the Moon – Ok Go. Bella and Jacob fixing motorcycles
17. Werewolves – Alexandre Desplat. Sam Uley and gang jumping from cliff.
18. Solar Midnite – Lupe Fiasco (iTunes Bonus Track). The song that is playing in Face Punch the movie.
19. I Need You – Alexandre Desplat. Jacob talking to Bella as Mike is sick at movie
    
20. Break Up -Alexandre Desplat. Bella confronts Jacob at La Push in the rain
    
21. Memories of Edward – Alexandre Desplat. Bella going to meadow by herself and finds Laurent.
22. Wolves vs. Vampire Alexandre Desplat. Laurent and wolf pack
23. Victoria -Alexandre Desplat. Bella’s fear of Victoria bubbling up while talking to Charlie.
24. Almost a Kiss – Alexandre Desplat. Jacob in Bella’s bedroom through the window. Shirtless of course
    
25. Done All Wrong  – Black Rebel Motorcycle Club. Bella at Emily’s house.
26. Hearing Damage – Thom Yorke. Charlie & Harry hunting wolves, wolves chasing Victoria, and Bella getting ready to jump. Also the best scene in the entire movie
    
27. Adrenaline – Alexandre Desplat. Bella jumping off the cliff.
28. Slow Life (With Victoria Legrand) – Grizzly Bear. Bella drowning.
29. Dreamcatcher – Alexandre Desplat. Hugging Jacob in the car outside house and Bella and Jacob in her kitchen.
30. To Volterra – Alexandre Desplat. Alice and Bella going to Volterra, and Bella running through the town to the clock tower.
31. You’re Alive – Alexandre Desplat. Bella and Edward reunited under the clock tower.
32. The Volturi – Alexandre Desplat. Bella, Edward and Alice see the Volturi and get their fight on.
33. Die Fledermaus – Duettino : Ach, Ich Darf Nicht Hin Zu Dir – APM Orchestra. (iTunes Bonus track) Elevator music on the way to visit the Volturi (”The Volturi track continues to play after they get out of the elevator)
34. The Cullens – Alexandre Desplat. Bella asks for a vote from the Cullens to join the family.
35. No Sound But the Wind  Editors. Edward driving Bella home.
36. Marry Me, Bella – Alexandre Desplat. In the woods, talking to Jacob, Edward and Jacob’s fight, and THE SUPER ENDING OF ALL TIME
    
37. Full Moon – Alexandre Desplat. End Credits.
38. A White Demon Love Song – The Killers. End Credits.
39. Meet Me on the Equinox – Death Cab for Cutie. End Credits.