In the US people have mineral rights to the earth under the surface of their property. This can be separated from the surface rights and sold off. If one buys just the surface rights, then the entity that has the mineral rights can, in most cases, access your surface to extract their minerals. Not reading the fine print on your title and having someone want to exercise their mineral rights is a serious issue in the US. I would definitely be very wary of buying land without the mineral rights.

But the right to use water that lands on your property? Never heard of "rain water rights". Unless it was previously declared somehow, forcing you not to collect rainwater would highlight the need for the right to bear arms. I would like to know more about how that came about in those cases.