The Minnesota Department of Natural Resources allows free camping on state forest lands. While there are no amenities, you can choose where you want to set up camp. Most of the state forests are in northern Minnesota but there are also a handful in central and southern Minnesota as well. You can find a map of Minnesota state forests at the Department of Natural Resources' "Find a state forest by location" webpage. There are other formal campgrounds in the state forests but they charge a fee.
Two national forests in Minnesota offer free dispersed, or primitive campsites. In northern Minnesota, the Chippewa National Forest offers hundreds of sites, most not accessible by car, and most without amenities like fire pits or latrines. Superior National Forest, also in northern Minnesota, also has primitive campsites, also not accessible by car, though, unlike the Chippewa sites, some do have fire pits and latrines. Both national forests offer a wealth of outdoor activities, with fishing, hiking, canoeing, and star gazing some of the top activities.
Enjoy free camping when you experience the 277 miles of hiking along the Superior Hiking Trail. The trail, which goes from Duluth to the Canadian border, has 82 backcountry campsites available during your hike. Parking lots every five to 10 miles make it easy to make a day hike to get to your free campsite.
The Cabela's stores in Rogers and Owatonna have dump stations and allow RV overnight parking. Also, the Cracker Barrel restaurant in Lakeville offers RV overnight camping. These campsites are really only free overnight parking spots and offer no showers or water hookups. Campers can usually use the store's restrooms during open hours, however.