During Southwest's fall fare sale through Friday, June 5 (an extension of one day due to SW's technical difficulties online), you can get fares from $49 to $123 each way on nonstop flights from MSP to Chicago, Denver, Phoenix, Kansas City, and Milwaukee. The sale is only good on nonstop flights between Aug. 25 - Dec. 16. The cheap airfares are not valid for travel on Fridays or Mondays and Sept. 3-5, Sept. 7, and Nov. 20-Dec. 1.
In a quick check, I had no trouble finding one-way airfares from Minneapolis St. Paul terminal 2 airport (MSP) to Chicago, Milwaukee, and Kansas City for $49 each way, Denver for $83 each way, and Phoenix for $123.
I may have missed a nonstop destination or two from MSP on Southwest, so check the map if you know of other nonstops from MSP on Southwest other than the 5 I listed. They would also be discounted.
Airfares must be booked by Friday.
It never hurts to see if other airlines such as Delta may be matching prices, but as of this morning I did not see any similarly low-priced fares on Delta.com to the same 5 destinations. Note that Southwest allows two checked bags at no extra cost while Delta charges $25 for the first checked bag on domestic flights.