In Nevada, rancher Cliven Bundy thinks that the state of Nevada does, but whether it does or not, he thinks that effectively he can use it if he wants to without paying anybody any fees to do so, although I gather he thinks this because he thinks that his grandfather was given some right to use it in perpetuity back in the 1880s, that is, the federal Bureau of Land Management (BLM) land he has been grazing his cattle on for the last 20 years or so without paying required fees, now piled up to about $1 million or so that he has not paid. So when his cattle were corralled by the BLM for Bundy's non-payment of said fees, a bunch of his armed friends went and successfully demanded that the BLM release his corralled cattle, which the BLM did, afraid of any violence that might ensue. So, even though all the other cattle ranchers in Nevada who use BLM lands are paying their fees, Bundy does not. Does he have any basis for his claims?
No. But why is that?
The problem is that he and many others, including the followers of the 1970s-80s "Sagebrush Rebellion," are under the impression that somehow unowned land belongs to the states, and that at some point the federal government simply took all that land from the state of Nevada without paying for it. Needless to say, what is owned by the federal government in Nevada is well over 80% of the land there, so this is nontrivial there, with only Alaska having a higher such percentage. Of course, the Sagebrush Rebellion, and now Bundy and his friends, have gone further and simply asserted that the federal government has no right to own any of that land, indeed that the federal government "does not exist," (or maybe "should not") although some of the Sagebrush Rebellion crowd went further and agreed with the old Posse Comitatus group that held that the same holds for the state governments also. For the old Posse Comitatus, the highest level of legitimate government in the US is actually the counties, hence "posse" for those who work with a county sheriff (when I worked for the State of Wisconsin Department of Natural Resources in the 1970s, Posse Comitatus members would make "citizens arrests" of DNR officials attempting to enforce fishing restrictions in state-owned lakes on them). I gather that Bundy has so far not made that argument, although at times he seems to have suggested that the land he grazes his cattle on belongs to Clark County, where Las Vegas is, and one of his more vociferous followers is a retired sheriff, maybe an old Sagebrush Rebel, the guy who was supposedly going to put his family members in front of the group as "shields" against the supposedly illegitimate BLM agents.
Indeed, the ultimate problem here is pretty murky, but for better or for worse legally speaking, outside the original 13 colonies unowned land, that which has never been legally owned by any private party in the past, belongs to the federal government. Within the original 13 colonies, it is indeed the states that own never-privately-owned, or "unowned" land. Why that should be is a matter of how long the entity has existed that initially owned the land, and as the original 13 colonies existed before the United States did, that this is why it is that the states succeeding those colonies are the owners of unowned land in those original 13 colonies, in contrast with the rest of the country. The claim that these colonies or states owned it rather than the native Indian tribes ultimately comes down to some sort of claim that the tribes never legally organized themselves to "own" it, and that the Crown of England had the right to grant it to the colonies instead.
Thus, outside the original 13 colonies, where one finds land that was owned previously by private parties with that ownership originally established by another European nation besides Britain or the US, then the laws of that other nation determine the land tenure property rights system that underlies that property, with the notable exception again of American Indian tribes, this reflecting the ultimate fundamental land grab of North America, with the tribal reservations granted to them specifically by the US federal government subsequently on case-by-case basis (although in some special cases such reservations or grants were made by colonies/states, most notably in Virginia where the tribes remain unrecognized by the US federal government, and certain tribes give the VA governor turkeys and other game on Thanksgiving to satisfy a 1680s era treaty between themselves and the governors of Virginia). It is only European nations and their legal land tenure systems that count.
So, there is land in Wisconsin that is legally governed by French land tenure laws, mostly along the Wisconsin River near Green Bay, where the Fox River dumps into Lake Michigan, and also near Prairie du Chien, where the Wisconsin River dumps into the Mississippi. Such land is organized in long strips that front on the rivers, in contrast with the checkerboard pattern established by the US Northwest Territory laws in 1787. Such land tenure laws also hold for underground land tenure rights near St. Louis, and also for most land in Louisiana. Likewise, in New Mexico there is land that has been passed down through private owners since prior to the 1848 Mexican War that is held according to old Mexican land tenure laws that descended from Spanish land tenure laws based on the 1390 Alfonsin Code of Spain, later replaced by the Napoleonic Code, but only after Mexico and most of Latin America gained independence from Spain, one of those minor problems with the original "Legal Origins" paper in the QJE by Glaeser and Shleifer that has been cited up the wazoo but that is simply crawling with such historical mistakes.
In any case, this matter of the 1848 transfer from Mexico to the US is what is at issue in Nevada where Mr. Bundy has been making his claims. When that happened, unowned land fell into the hands of the US government without having to be bought or otherwise transferred from a county or state government. The Homestead Act under Lincoln in the early 1860s and subsequent ones laid down how private individuals could turn such land into their privately owned property by working such land for sufficient periods of time in certain ways, but over 80% of land in Nevada was so crummy that nobody ever did so, including the sections that supposedly Bundy's grandfather grazed cattle on at times. So it remained and remains federally owned, even if somehow Bundy thinks that his grandfather ought to have been given title to it, although that is not precisely his claim, which amounts to a muddle between he ought to have usufruct rights and that it is or should be owned by the state of Nevada, or maybe by Clark County, and if so, they would grant him those usufruct rights to graze without paying any fees. But none of that is true and has been repeatedly ruled as such by the courts.
I note a peculiar example of this matter of unowned land in Virginia, where many years ago I worked briefly on land use management for the George Washington National Forest here in VA. So, there is an agreement between the US Forest Service and the Commonwealth of Virginia regarding unowned land within the boundaries established for the George Washington Forest regarding such land within those boundaries. It is that if the Forest Service bears the transactions costs of establishing what the precise boundaries of any such land are and that the land is indeed truly unowned, then the state will transfer its ownership of that otherwise unowned land to the US Forest Service. I am not sure about now, but as of 30 years ago there was somebody in the office of the George Washington National Forest HQ part of whose job was to do this with this leading to about two pieces of land per year being so transferred, most of these rather small, a few acres, but also mostly odd bits of forest back in the mountains that most people around it probably thought was owned by somebody privately. But, in fact, by whatever historical fluke, the pieces never did come to be owned by any non-Indian private parties and thus was owned by the Commonwealth of Virginia.
In any case, Cliven Bundy does not have a legal leg to stand on, and the various politicians and commentators jumping up and down and screaming on his behalf should just cut it out.