Gry Bagøien and her band, Æter. Danish electronica, verrry obscure, even in Denmark. I’ve never been to a concert, being stuck in America and all, but her music is at times trippy, sad, playful and surreal. The lyrics are usually English, often Danish and sometimes, both in the same song. She worked with FM Einheit, formerly of the Einstürzende Neubauten, a better-known band, at least in Germany. Really cool.
Definitely dredg. I think anyone who liked Tool’s superb Lateralus would go for dredg and their CD “Leitmotif.” Both of the two people who borrowed my dredg CD were big Tool fans, and both immediately ran out and bought Leitmotif. Go to http://www.dredg.com and download “Of the Room,” which isn’t on Leitmotif, and/or go to Amazon and check them out. You won’t be disappointed.
Additionally, there is a band called pete. (lowercase with a period) who’re pretty good. A little more popular oriented, but definitely easy to rock out to. They can be found at http://www.petenoise.com. If you want to try to download a song or two, which I think is hard because they’re kinda obscure, go for “Sweet Daze” or “All Love is a Lie.”
Last is the band Onesidezero. The lead singer’s voice is eerily similar to that of James Maynard Keenan, Tool’s lead singer, and the music is also like Tool’s, a little. Their best songs are “Awake,” “Soaked,” and “Tapwater.”
I’ve seen Great Big Sea in concert! They kick ass. But then I just quit Irish dancing after having done it for 2 1/2 years, so I guess I’m a bit more immersed in Irish music than most.
My vote: The Jennifer Nettles Band (formerly Soul Miners’ Daughter)
I’ve seen GBS twice, once about 5 minutes from my house…so there 
On a celtic theme…The Drovers from Chicago…
To really rock your world though, check out La Bottine Souriante
Hard to pigeon hole their music…their CD cover describes it as “popular Acadian-French traditional songs flavoured with Celtic, Latin salsa, and New Orleans style swing jazz”…seen live, they are fantastic…the guy providing the feet percussion is amazing…
Crack the Sky rocks.
Listen to “I Don’t Have A Tie” and have your mind blown.
NOW!
Heard of them and heard them. They’re okay. My brother likes them, I wasn’t too impressed though.
I’ll say Built to Spill. They’re a good band that no one but me seems to have heard of. No one at my school has, at least.
A few months ago I would have said Dashboard Confessional. But now they have a music video and I hear them on the radio every now and then. I still like them though.
The Grapes !!! Also a plus they pass out ballons at there shows
Odd, I haven’t heard of any of these bands…
Kara’s Flowers is a band I saw in LA a couple years ago. Don’t know if they’re still going, but they’ve released an album. Very well-written, well-played music.
Are we limited to only one? 'cause I could go on here for a couple hours listing bands. Going for music-that-others-might-not-like-but-wish-the-band-were-more-recognized line, Man or Astroman .
The (understandably) rather domestic-market oriented bands of Japan can boast of scads of bands andartists that should be on the cover of Rolling Stone, but I’ll mention only The Sherbets , led by members of the old Blankey Jet City.
Y’all heard of Yonder Mountain String Band?
Great bluegrass. I loves them.
Didn’t they do “Radar Gun”?
Bind. Thay are small known band in Indianapolis. Alomst nobody has heard of them, but htey are really good if you liek the heavy metal scene. http://www.bind-online.com/
The band is called SHU
Here’s a link, please listen and let me know what you think.
http://artists.mp3s.com/artists/93/shu1.html
Honey
How 'bout The Bacon Brothers?
Purveyors of fosoroco.
(Thats folk, soul, rock, and country)
BTW One of 'em is Kevin Bacon.
Kayak
A Dutch band of the seventies/eighties, a bit in the style of Pink Floyd and Yes. They are actually back together again now.
Underfoot , Va Beach group. Saw them three times over the last few years. Impressed me.
Five Americans 
Monopot , a Norwegian post-rock trio. I have never met anyone else who has heard of them. “Something is liek nothing was” is a quite astounding album.
Foremen. American political humor folk.
Ahem… shameless plug
tsk tsk tsk