I don't know that these are my favorite sad songs, but they came to mind first...

Sia - Breathe Me
The Carpenters - Rainy Days and Mondays
Sarah McLachlan - Adia
Counting Crows - Colourblind
Todd Rundgren - Can We Still Be Friends

Though of some more...
Fleetwood Mac - Landslide
James Taylor - Fire & Rain
Coldplay - Fix You
Coldplay - The Scientist
Ben Folds Five - Brick
Sinead O'Connor - Nothing Compares 2 U
Dionne Warwick - Anyone Who Had a Heart

1.Evanescene-My Immortal
2.Jesse McCartney-Because You Live
3.Paramore-When It Rains
4.Avril LAvigne-When You're Gone
5.Mandy Moore-Only Hope

HONONARY MENTIONS:
Jojo-Too Little Too Late
Selena-Dreaming Of You
Carrie Underood-Just A Dream
Carrie Underwood-So Small
Kelly Clarkson-Because Of You
Christina Aguilera-Hurt
Aaliyah-I Miss You

Hinder - Lips Of An Angel
Hinder - Better Than Me

Oh..I forgot..:

- Toni Braxton - Unbreak my heart
- Imogen Heap - Speeding Cars
- Imogen Heap - Hallelujah
- Sixpence None the Richer - It came upon a Midnight Clear
- Flypside ft. Tatu: Happy Birthday

1. A Perfect Circle - "3 Libras"
2. Guns N' Roses - "November Rain"
3. The Smashing Pumpkins - "Spaceboy"
4. La Ley - "Más Alla"
5. Hole - "Dying"