I've got TONS! I'm really into indie/folk right now so a lot of these songs aren't mainstream (oh, and a few of them are repeats), but here goes:
Twilight:
Rebecca St. James - Lion
Yiruma - River Flows in You
Vanessa Carlton - Twilight
Coldplay - A Message
Parachute - Kiss Me Slowly
Snow Patrol - Crack the Shutters
Secondhand Serenade - Stranger
Angels & Airwaves - Breathe
Blue October - Calling You
Blue October - James
Blue October - Quiet Mind
Phoebe Sharp - Poison Love
Saving Jane - I'm in Love with a Vampire
Nicole Chittle - Edward
New Moon:
Shannon Thomas - Edward
Something Corporate - Break Myself
Blessid Union of Souls - Standing at the Edge of the Earth
Vienne - She Breaks
Framing Hanley - Alone in this Bed (Capeside)
Kari Kimmel - Dreamer
Daphne Loves Derby - Pollen and Salt
Evanescence - Hello
Erin McCarley - Pitter-Pat
Trading Yesterday - May I
Mat Kearney - Breathe In, Breathe Out
The Swell Season - If You Want Me
Mat Kearney - Lifeline
Jack's Mannequin - Swim
A Fine Frenzy - Near to You
Matt Nathanson - Lucky Boy
A Fine Frenzy - Almost Lover
Ryan Star - Last Train Home
Celica Westbrook - New Moon
Kelly Clarkson - Haunted
Blessid Union of Souls - My Friend
Superchick - Beauty from Pain
Melissa Etheridge - Breathe
Pixie Lott - Broken Arrow
Evanescence - October
Shannon Thomas - Don't Be Beautiful
Age of Information - Tell Her Something
Red Roses Black - I Miss You
Phoebe Sharp - Guess
Eclipse:
He Is We - I Wouldn't Mind
Lesley Roy - Dead but Breathing
The Spill Canvas - Secret Oath
The Red Jumpsuit Apparatus - Your Guardian Angel
Dashboard Confessional - Hands Down
Staind - Believe
Parachute - She is Love
SafetySuit - Anywhere but Here
Lights - Drive My Soul
Mayday Parade - Miserable at Best
Straylight Run - Existentialism on Prom Night
Dashboard Confessional - The Shade of Poison Trees
Green River Ordinance - Learning
Graham Colton - On Your Side
Gary Allan - The One
Blessid Union of Souls - Hold Her Closer
Snow Patrol - You Could Be Happy
Lyndzie Taylor and Mallory Trunnell - Compromise
Green River Ordinance - Uncertainly Uncertain
Breaking Dawn, Book 1:
H.I.M. - Vampire Heart
Shannon Thomas - Unbelievable
Parachute - The Mess I Made
Blue October ft. Imogen Heap - Congratulations
RyanDan - Like the Sun
Cat Power - Sea of Love
Death Cab for Cutie - Soul Meets Body
Dashboard Confessional - Vindicated
Something Corporate - The Runaway
Breaking Dawn, Book 2:
Kris Angelis - The Cradle Will Rock
Parachute - Strange World
Green River Ordinance - Out of the Storm
Parachute - Under Control
Trading Yesterday - Beautiful
Something Corporate - Only Ashes
Something Corporate - Ruthless
Dashboard Confessional - These Bones
Dashboard Confessional - Clean Breaks
Mat Kearney - Crashing Down
Matt Nathanson - I Saw
Matt Nathanson - Kept
Anberlin - Impossible
Anberlin - Breaking
Skillet - Comatose
Flyleaf - All Around Me
Breaking Dawn, Book 3:
Blessid Union of Souls - Scenes from a Coffee House
Blessid Union of Souls - Forever for Tonight
Taylor Swift ft. The Civil Wars - Safe and Sound
Green River Ordinance - Piece it Together
Liz Akhavan - Lullaby
Missy Higgins - Nightminds
The Pogues - Love You Till the End
Green Day - Last Night on Earth
Muse - Invincible
The Cinematic Orchestra - To Build a Home
Jimmy Eat World - Firefight
Mat Kearney - Won't Back Down
Mat Kearney - All I Need
RyanDan - Tears of an Angel
Midnight Sun:
Age of Information - Outside
Age of Information - Break Your Heart
Green River Ordinance - Inward Tide
Aqualung - Strange and Beautiful (I'll Put a Spell on You)
The Afters - Beautiful Love
Trading Yesterday - Love Song Requiem
Andrew Belle - In My Veins
Trading Yesterday - The Beauty & the Tragedy
Thriving Ivory - Angels on the Moon
The Spill Canvas - Under the Covers
Goo Goo Dolls - Iris
Something Corporate - As You Sleep
SafetySuit - Someone Like You
Teitur - One and Only
Boys Like Girls - Hero/Heroine
The Spill Canvas - This is for Keeps
Parachute - She (For Liz)
SafetySuit - Find a Way
Secondhand Serenade - Awake
The Spill Canvas - Lullaby
Trading Yesterday - She is the Sunlight
Death Cab for Cutie - I Will Follow You Into the Dark
Should help everyone fill in their playlists a little.
Enjoy!