I am terrible at classifying music, so I apologize if what I say below isn't quite what you expected.
According to iTunes, everything I've listed below is "alternative," but I feel like they're all quite different. Here are some of my faves:
1]The Decemberists ~ there's an audio player on the far left: link
^^I love their rock opera album, Hazards of Love, and their story-form album, The Crane Wife, most of all.
2] The Swell Season/Frames/Glen Hansard ~ A Youtube Playlist link
^^I heard Glen and Marketa in the movie Once and have been in love with their music since then.
3] Mumford and Sons
4] Jump Little Children: JLC was the best! But they no longer play. Here's a Youtube playlist: link
4b] Jay Clifford: While JLC is dead, the lead singer Jay is still performing solo. Youtube playlist: link
1] The New Pornographers (with Neko Case) ~ link
2] Civil Twilight ~ link
3] Editors ~ there official site is currently down, but you can listen on Myspace: link
4] Block Party ~ link
1] MUSE ~ they deserve their own category in my heart