I think my music tastes might differ a bit from most of the people here (I listen to a lot of folk/singer/songwriter stuff), but for the sake of sharing:
Vienna Teng: Probably one of my all time favorite artists. She's a really great singer/songwriter and pianist. She is an Atheist and does bring it up at concerts from time to time:
I would not even consider that her best song, but it's the only one that mentions Atheism directly. Some of my other favorites
her cover of Damien Rice's "Cannonball": http://www.youtube.com/watch?v=-_Z-Cs8kst8
Her song Passage ( which is a capella) is probably the best example of dealing with death and grief in a non-religious way that I have ever come across in music. : http://www.youtube.com/watch?v=RiMsI5ZZ-qg
There is a British folk group called Noah and the Whale (I'm not entirely sure what's up with the name), that has the song Peaceful the World Lays Me Down. I know virtually nothing about the band, but when I first listened to the song it really stood out as having Atheist sentimentality. It's probably not a music style for everyone, and it is a bit mopey at first. I'd say give it a listen all the way through, just to give it a chance. I would link it, but I can't find any videos of the album version available in my country.
A side from the folky stuff, I'm also a metal fan.
I'm a big fan of the band Otep. The song "The Lord is my Weapon" is pretty powerful, though it's more anti-organised religion, than just religion in general.
I'm not 100% sure on the beliefs of the band members, but the lead singer is a Taoist.
The metal band Celeste has a lot of anti-god lyrics, but they are all in french. :)
honestly, a lot of European metal has a very strong "anti god" mentality to it, if your into that style of music.
Lastly, the song "Roll Away Your Stone" by Mumford and Sons was actually linked to me by an Agnostic friend who said he found it could be interpreted from a freethinker's point of view. I do see what he means (minus the "soul" part).
All the rappers of Odd Future are atheists except Frank Ocean. Musicians that sing about atheism are the artists of http://wergrandunified.com/
Atheist love song...
Let me know what you think!