Ohh, I'll have to check out some of these bands. As for me, the best bands I've ever heard are as follows:
The Decemberists - Masters of storytelling, often with an old English spin. They rock hard, as heard in their 13 minute song - "The Island/Come and see/ The Landlord's Daughter/You'll not feel the Drowning", or their classic rusty sweet alt-bluegrass rocker "Chimbley Sweep". They take it slow on songs like "Eli, The barrow boy", and "Los Angeles, I'm yours" and still can get me tapping toes. And throughout it all, their lyrical brilliance consistently outshines nearly all other artists I've ever heard. I'm talking goosebump-inducing stuff, here.
Sufjan Stevens - Here's some music at the opposite end of that spectrum. Sufjan (Pronounced soofyan), like Colin Meloy (Lead singer for the Decemberists) has a degree in Creative Writing - and it shows. He's a Christian singer, and he touches on those subjects, but with an honest and (sometimes brutally)objective viewpoint. Highly recommended songs include "They Are Night Zombies!! They Are Neighbors!! They Have Come Back From The Dead!! Ahhhhh!", "Come on! Feel the Illinoise!", "Chicago", and if you're confident enough shed a tear or two, "Casimir Pulaski Day".
The Magnetic Fields - My first foray into non-mainstream music. I've been listening to their songs for over a decade, and I'm still not tired of them. They are the the masters of texture, as heard in songs like "Suddenly, There is a Tidal Wave", "All My Little Words" and "Take ecstacy with me". Other just plain great songs are "Underwear", "The Luckiest Guy on the Lower East Side" and "Absolutely Cuckoo".
Other honourable mentions are the bands Neutral Milk Hotel, The Fiery Furnaces, Animal Collective, Vashti Bunyan, Ben Folds(Five)