Minnesota has a pretty good hip hop scene... I probably need to stop mentioning these same groups everytime these threads come up... but they are so worth a listen. :)

Atmosphere - Nationally and world known to any real fan of hip-hop, but refuse to ever sign a record deal so you'll never hear them on clear channel stations. Have their own record shop, their own label with other fantastic music, and put out tons of great albums. Made up of two guys from Minneapolis, Slug, the vocalist, and "Ant", the beatmaker/producer.

http://www.youtube.com/watch?v=wMNNwa46Plg

http://www.youtube.com/watch?v=84nqfhmo3tA

http://www.youtube.com/watch?v=Ekivast3QX0

Brother Ali - On the label Atmosphere started, Brother Alis production and beats are also done by "Ant" from atmosphere. So if you like them, you'll probably like Brother Ali. He's white, was born an albino, and is also a Muslim. Makes from some really interesting hip hop and a different style of lyrics.

http://www.youtube.com/watch?v=JojHV4pAWDg

http://www.youtube.com/watch?v=6ScPoBEFl1Y

Doom Tree - Another great local hip hop group, but refer to themselves as a "collective" as there is like 8+ members of the group.

http://www.youtube.com/watch?v=DQhRQ8BI0gA

For non hip-hop...

Trampled by Turtles - bluegrass/folk band. Lots of guys with fiddles, mandolins, guitars, and of course beards and plaid. Great band to see live, has some pretty good stuff out. A little "jammy", a lot folk, and a lot of fun. Gaining more and more attention nationwide.

http://www.youtube.com/watch?v=Xjdkc14-zwQ

The Replacements - One of my all time favorite groups. Takes a little "aquired taste", but I love them, and the song I linked is one of my all time favorite songs out of anyone ever. The piano, his voice, it's all just perfect. They disbanded in 1991.

http://www.youtube.com/watch?v=f8J9WssSj7Q

The Artist Formely Known as Prince - LOL.

Also Bob Dylan is from here, but I think everyone knows who he is...