Aside from agreeing that the poll is pretty terrible, here's my list:
Pinback: some of their songs can be a little to wispy, atonal, and unmelodic for my tastes, but clever lyrics and some really great songs make them worth a check out. Much more on the acoustic side, with less powerful vocals, they're still very entertaining. Some of their songs take getting used to, but stay with it, because it's worth it. I recommend listening to "Penelope", "Non-Photo Blue" and "Fortress"
Single File: probably a little less indie than when I first heard about them (local band), but still good. Listen to their early stuff (off of the album "No More Sad Face") before anything else. Their song "Mannequin Loveseat" is either the most spot-on parody of overly emotional music (not emo necessarily, just the "my girlfriend dumped me, wah" that's evident in many genres), or completely serious; hilarious either way. They don't take themselves seriously, and (at least in their early albums) embrace self-deprecating lyrics. I recommend "Zombies Ate My Neighbors", "Grocery Store", "Velcro", and "Everything"
The Hush Sound: I've got a thing for rock songs with piano elements, what can I say? Thoughtful, clever, lyrics, combined with some normal rock, make for a fun experience. Not the most out-there band, but somewhere between purely commercial crap, and stuff that's trying too hard to be different. Powerful vocal talent, and never difficult to understand. I recommend listening to "Wine Red", "Weeping Willow" and "Don't Wake Me Up"
Tickle Me Pink: another local band (for me). Closer to pure rock than many indie bands, but a good listen. Not much else to say. Still a bit unpolished, but they'll either get much better or become terrible. "Typical" and "Expiration Date" are good first listens for a feel of their style. The latter is closer to an indie feel, the former is more of an emo-rock thing.
Electric Six: exceptionally funny lyrics, and often a dissonance between the upbeat nature of the instruments and more dour nature of the lyrics. Once again, piano in rock songs, yay. Closer to electronic/techno, but without losing the ability to listen to the music. I recommend starting with their cover of "Radio Ga Ga", "Lucifer Airlines", and "Dance Commander"
VAST: (it's all upper-case, since it's an acronym) independent hard rock. Thoughtful and deep lyrics, sung without becoming inaudible due to screaming, given a more rock-ish feel. Some of the songs can be a bit disturbing (watch the video for "Pretty When You Cry" at your own risk), but generally a good fit for the less introspective side of indie music. Still filled with meaning and emotion, just less wispy and melancholy (or, at least, less wispy). Much more on the expressive, rather than introspective, side of emotions. I recommend "Touched", "Lost", and "I Don't Have Anything" for a good first taste
Scapegoat Wax: Good music, made with a more hip-hop/rock feel than most of indie music. Self-deprecating without approaching self-pity, the lyrics come close to an anthem for someone who knows they're a bit shy, or out of place. Poppy at times, but not without losing the humor or intelligence. I recommend "Aisle 10 (Hello Allison)", and "Lost Cause"
Roe: a third hometown band. I promise to stop eventually. Verging closer to emo, but without getting pitiful, or really self-absorbed. Solid pop-rock, more on the acoustic side (think "Iris" by the Goo Goo Dolls, for comparison, if you must). Not the deepest music I've ever heard, and some of it really needs to grow on you (there's some atonality at times which you come to appreciate). I recommend "Mayday" and "Everything You Are"
The Good Luck Joes: a more mature band, with a bit more subtlety to their lyrics and instrumentation. Not as purely emotional, and with a bit more sheen than might be appreciated in an indie band, they have great lyrics, solid vocals, and nice rhythms. Some of the rhymes are simplistic, but still fun. They sometimes alternate between truly morose songs (like "Thin Air"), and still-thoughtful and somewhat melancholy, but less abjectly sad songs. For comparison, they're perhaps a more mature, slightly older, All-American Rejects. I recommend "You Can Never Go Home", "Thin Air", "Middle of Me", "The Sun Explodes", and "Always Be Around"
Dirt Poor Robins: rather Christian, but you might not notice it on the first pass. Some of their songs are pure pop ("Love Again" sounds rather insubstantial on the first listen, but if you pay attention it's actually much deeper). Happy songs, bracketed by more introspective ones. Very reliant on powerful voices to carry the songs, but it works. There seems to be an odd ambivalence about the mood of their debut album, shifting between songs about love coming to fruition, and much more dour songs, but it plays well. I recommend "Someone" (for a taste of the melancholy), "Love Again" (much happier), and "When All Is Said And Done" (somewhere in the middle).
Carbon Leaf: a very Irish feel, with some songs that are downright jig worthy. They have the tendency to be very hit or miss. Their songs either work wonderfully, and both entertain you and make you think, drawing you out into a different mindset, or their songs are atonal, annoying, and terribly pretentious. That said, "Life Less Ordinary" is probably one of the best songs about being lovestruck I've ever heard. In addition to that, I recommend "What About Everything?", "On Any Given Day", and "The Boxer"
Kate Nash: not really indie per se, but a very indie feel. Thoughtful, introspective, lyrics, with a polish of actual pop sensibilities. Manages to take the good parts of Regina Spektor, and the Polyphonic Spree, and condense them into something better than both. From the former, she gets thoughtful songs, with simple instrumentation, supported by her depth of emotion and vocal prowess. From the latter, she gets enough rhythm to counteract the occasional atonality of the former. Listen to "Foundations" (which has gotten some airtime here in the States), as well as "Mariella". You'll need to listen to "Mariella" a few times to really appreciate it, but it has both down-to-earth melancholy, and pure, giddy, fun.
The Dresden Dolls: again, not purely indie, but very off the beaten track. Only a piano, and a set of drums (as well as the lead singer). Fun songs with tinges of sadness and deep understanding. They never get too full of themselves, and seem to punctuate any moments of philosophy with moments of bashing themselves (as in "Dirty Business"). Amanda Palmer doesn't pull any punches with her lyrics, or the way she sings them. I recommend "Dirty Business", "The Shores of California", and "Coin Operated Boy"
Amy Studt: a one-woman band, who manages to be both pop-oriented and surprisingly thoughtful. Her first album, False Smiles, while revealing her youth, combines hopeful themes with a rather sober and somber understanding of the world around her. A high-school mentality permeates some of her early work, which makes perfect sense, but much (if not most) is transcendent of that. Her early happier songs can come off as a bit too earnest, but if you can shelve cynicism for a moment, the lyrics and music really are good. Her newer album, My Paper Made Men, is a much more mature effort, with a depth of sadness in some songs that can only come from the passage of time. If listened to in order, her sophomore effort sounds like the slow process of overcoming a bad relationship, which (while cliched) she does in a very compelling way. I recommend: "Furniture", "Nice Boys", "Ladder In My Tights", and "Superior Mind". The first is a sad song, backed only by acoustic guitar; the second is a much more upbeat song, essentially declaring her independence from men, a pure girl-rock anthem, but fun to listen to; the third is almost pure saccharine, but without being manufactured (so, sugar-cane, if you will), fun, reaffirming, and hopeful; the last is dour with a hint of hopeful transcendence. The fact that I've written so much should convey my level of recommendation of her.
And here's a list of individual songs I strongly recommend:
"Man of Devotion" by Fools Garden
"You Know So Well" by Sondre Lerche
"Straight Lines" by Silverchair
"Don't Trust Me" by 3oh!3
"Lean On Sheena" by The Bouncing Souls
"In The Kitchen" by Umphrey's McGee
"'Cause You Can" by Birdmonster
"Perfection Interrupted" by Leeni (seriously, get this one)
"Lifelight" by Andy Hunter
"Jump Start" by The Hangups
That's a lot of words, huh?