The answer to the question may surprise you. In the U.S., you generally don’t buy your burial plot. You buy burial rights or an easement. For purposes of this post, burial rights includes entombment, inurnment, and any other form of being a permanent resident of a cemetery. Outside the U.S., you often only rent the burial plot. For example, my relatives who were buried in Germany no doubt lost their spots when the family stopped paying to renew the rent. In those cases, the remains are usually dug up and deposited in an area set aside for the purpose.
I haven’t studied all 50 states, but of the states I studied, none have laws that address you actually buying the plot. They have laws concerning certain aspects of burial rights. For example, you may have to get permission from the cemetery to resell the burial rights if you decide to do so. In general, the cemetery dictates how you can resell the burial rights for a plot. In some cemeteries, they don’t care as long as you notify them of the change in whose going to be buried there. In other cases, the cemetery has to approve the transfer. In at least one cemetery in New York, they will only let you sell the burial rights to another person who was born in the town or has lived there long enough because the town’s cemetery is getting full. In some cemeteries, you can only sell the burial rights back to the cemetery and usually at the price originally paid.
I found a number of cemeteries where you have to be of the religious faith of the cemetery (Roman Catholic, Islamic, Jewish, etc.) with some cemeteries making exceptions for a spouse or children of a different religious faith, but some cemeteries won’t make an exception. In one famous example seen on some blogs, a Protestant who married a Catholic were buried adjacent to each other, but the Protestant was buried in the part of the cemetery that allowed Protestant burials and the Catholic spouse was buried in the Catholic section of the cemetery. You can read more about this case at: http://www.academia.dk/Blog/the-graves-of-a-catholic-woman-and-her-protestant-husband-holland/. You can see a photo of it on Google Maps. Look for the pin labeled Graf met de handjes. You may have to zoom to aerial view.
If you get what appears to be a burial plot deed, read the fine print and also your state’s laws on the subject. In one case, I have seen plot deeds which sound like you are buying the plot, but state law made it clear you are only buying burial rights.
This is important for another reason: the cemetery may also limit what type of headstone you can place in it. http://www.everlifememorials.com/v/headstones/regulations-cemetery-headstones.htm is a great example of some ways cemeteries can limit your headstone choices.
The above link includes a number of questions you should ask. Do this before you buy burial rights in a cemetery and definitely before you need to bury somebody there if you haven’t previously checked into what the cemetery allows/doesn’t allow. Also, don’t assume that just because the cemetery has some of the rules and regulations posted on their grounds, those are the only ones they have. Be aware that most cemeteries include some kind of headstone setting fee; it may be included in the overall cost or it may be a separate cost. It can range from $50 to several thousand dollars although it’s unusual to see the cost go above a couple of hundred dollars for the average cemetery.