Belle and Sebastian
Broken Family Band
I can't really listen to any of them when I'm writing. No sirree. I start singing along and getting far too distracted.
My best ever, number one spot for band I can listen when writing is (drumroll please)...
Random, I know. I think they have just the right blend of tunefulness and familiarity and background warmth. I don't know why they never got more famous. I think they're great. Shame About Ray is the obvious place to start, but Come on Feel is very underrated I feel. And very good to write along to. Trust me.
(And when you've stopped writing, definitely listen to the Broken Family Band - Welcome Home Loser is a good album to start with).