It's very much about my taste in music so keep that in mind. ;) I'm not trying to say that this is the definitive list or anything, this is just my opinion.
1. Ed: U2 - I Still Haven't Found What I'm Looking For
It's not a big secret that I'm a huge U2 fan (Novemeber 23, squee!), but this song fits. It's about searching. It's about faith. It's about not giving up. The music is kind of mellow, but the sheer yearning in Bono's voice matches perfectly.
2. Al: U2 - I Will Follow
Another U2 song, because I thought it would fit nicely into the idea of them being brothers. Loud, fierce music and lyrics that are absolute perfection. They perfectly complement Al's dedication toward staying with his brother and his mother issues. "A boy tries to be a man / His mother takes him by his hand."
3. Roy: Blur - Beetlebum
It was really, really hard trying to come up with a song that I thought fit Roy, and this is the closest I could come up with. Dark, with an edge of forcefulness and sex. The chorus is just glorious as well. I don't think the lyrics quite fit, but the music is so beautiful that I couldn't find a better match.
4. Winry: The Beatles - I Saw Her Standing There
Energetic and poppy in that early Beatles way. Full of handclaps harmonies, and the trademark Beatles yowl, it's sexy and young in a way thinks really matches up with Winry's vibrancy. And I'm pretty sure that Winry's seventeen by the end of the series. ;)
5. Scar: The Clash - I Fought the Law
The Clash were a punk band, back in the day when it was actually considered rebellious to be in a punk band. Loud and vicious and angry. You can just see Scar going out to deconstruct some heads to this music. "I fought the law / And the law won."
6.Hughes: Moby - Rafters
Hughes is hands down my favorite character in FMA. Moby's music is all about soul, and this song is no different. There aren't really any lyrics, but the gospel humming and funky dance groove characterize Hughes' natural effervescence quite nicely. The song practically glows.
7.Armstrong: Daft Punk - One More Time
If "Rafters" glows, then this one sparkles. It's all celebratory lyrics over Neo-disco. "Celebrate being so free / One more time." Even with all that, you get the sense of a good beat and a bit of retro style. Hooray for French guys that dress up like robots!
8.Izumi: Fatboy Slim - Weapon of Choice
Best known for being the video that Christopher Walken danced in, "Weapon of Choice" has a dance groove and attitude to spare. Izumi is definitely one of my favorite characters, and she's as strong, tough and asskicking as this song is.
9.Hawkeye: Oasis - Supersonic
Hawkeye is teh sex. She really is. "Supersonic" is sexy in a casual, almost background way. It's loud, it's forceful, and it could kick your ass if you're not paying attention. It's just one of those songs. Get in its way, and you get run over. Not in a punkish way, though. In a "calmly puts three bullets in you an walks over your decaying corpse" sort of way.
10. Havoc: The Strokes - I Can't Win
Poor Havoc. He really does get shafted all the time. In both the manga and the anime. "I Can't Win" is all about rejection, something Havoc has plenty of experience with. The Strokes manage to pull off sounding vibrant and melancholy at the same time.
But where is character X (where X is a character not on the above list)? you ask. Well, ten songs is more than enough, so I stuck to my favorite characters. I matched up a ton more than just these.
Some other characters:
Radiohead - Optimistic: Bradley
The Pixies - Where is My Mind?: Wrath
NERD - Tape You: Lust
Stereophonics - Jealousy: Envy
Radiohead - Dollars and Cents: Greed
U2 - Mofo: Sloth
The Vines - Outtathaway: Gluttony
The Stills - Gender Bombs: Tucker
Coldplay - The Scientist: Hohenheim
Oh, and PLEASE DON'T HOTLINK AS IT MAKES ME CRY.