Two moody female singers dealing a lot with this subject are Jewel and Dido
Dido's hunter seems to match everything quite well released in 2001
Ooooh, Dido is an EXCELLENT choice. "Dont Think Of Me" is such a great song.
Another I remember is "Deathly" by Aimee Mann. But it'll probably be a tearjerker song.
I'm also a big fan of the Blue October song "Hate Me Today"
OOOhh, also Elliot Smith's "Somebody that I used to Know" - GREAT breakup song.
Elvis Costello's "I'm not Angry" is also a great track.
Kelis - "Caught out there" is great if the ex was a cheater
"Do RIght" by Jimmies Chicken Shack
"Last Goodbye" by Jeff Buckley
"Moment of Weakness" by Bif Naked (GREAT empowering song)
"Goodbye to You" by Michelle Branch is good too
"Black Eye" by Fluffy
"Judas My Heart" by Belly
I don't know what musical style you're looking for, and if you're looking for sad songs, angry songs, etc.....but some artists I'd definitely look into, as they have multiple great songs are:
Ani Difranco
Paul Westerberg
Elliot Smith
Mojave Three (Great breakup songs, but really depressing)
Fiona Apple
Archers of Loaf
Mary Lou Lord
Dixie Chicks (again, really depressing)
Bif Naked
Belly
Okay, lemme go hunt my list now.