Here's a good example of great indie songwriting that went hugely unnoticed.It's soft indie, the kind you would relax or fall asleep to. If you look into this you'd find some really well crafted and beautiful music.
The first solo release from Justin Vernon/AKA Bon Iver. Probably his most different release as he incorporates a bluesy feel and sometimes a harmonica in songs. Some songs are from his first band, Mount Vernon. It may not hold a candle to his later work, but it's definitely worth checking out if you're a fan of his music.
I'm an avid Listener of American Football and this band is the closest I could find to a reincarnation of them. I wouldn't say they're a rip off of AF, they just have the same twinkly guitar harmonies and great drumming. A must listen if you like that type of indie.
This is the solo project of the singer of the indie pop band Umbrellas. In my opinion there is a lot more emotion in these songs than anything the Umbrellas have done(though I still enjoy them). Some amazing lyrics as well as music can be found here.
Another talented indie band with some great and powerful lyrics and catchy music. Three of the songs are free to download on purevoume. Be sure to check out the song "The Vaccine". http://www.purevolume.com/papermachemusic/albums/Debts+to+Pay
Two of the members of this band were in The One Up Downstairs with Mike and drummer Steve from American Football. They also had a former drummer from Braid. Melancholy indie pop is probably the best description for it. Relaxing indie.