Michigan - Faygo
Faygo is perhaps best known nationally for being appropriated by Insane Clown Posse, but this refreshing Michigan soda's wildly popular in its home state for its multitude of flavors and relatively low cost. This could've gone to Vernor's as well, but Faygo is more ubiquitous throughout the state and is still made in Detroit, so it comes out on top.
Minnesota - Sun Drop
This citrus soda may've been introduced in Missouri, but it's got a strong foothold in Minnesota and the upper Midwest.
Mississippi - Barq's Root Beer
Barq's was invented in Louisiana, but first sold in Biloxi, Mississippi, when its founder moved there in 1897. That's some old-timey root beer.
Missouri - IBC Root Beer
Once Missouri's most famous soda company, IBC is now owned by Dr. Pepper Snapple Group, but that doesn't make its eponymous root beer any less delicious.
Montana - Flathead Lake
This one's pretty niche, but Flathead Lake produces "gourmet" sodas out of Montana in flavors like huckleberry and sour cherry.