Looting is a huge problem for archaeologists, for a couple reasons. Let's look at the problems and then see the laws which are in place to solve them.

First, looters/pothunters/grave robbers damage archaeological sites and remove important context from the items. An archaeological item that has not been excavated is no longer tied to anything, cannot be properly dated, and contributes nothing to the understanding of the culture that used it. If it was still in context, it could offer information based on what other artifacts it was found with, where in the site it was found, and can thus be used in an academic manner to learn things. Looting damages the site (because looters do not care about context, but just destroy things to get to the artifacts). You don't even know what site it came from.

To see an example of the incredible damage that occurs from looting, check out this picture of a site in Iraq. All those divots are holes where people are digging around with no care or record keeping. Archaeology can only be done once. There are no second chances to re-excavate something. Looting means knowledge is gone forever.

The only reason people loot is because people want to buy the things. Demand forces supply. Supporting the antiquities market by buying antiquities, whether they are licensed or not, nevertheless creates a demand where people see these things selling for money, think "I like money" and destroy sites trying to find artifacts they can sell. It's a vicious cycle. The looters themselves are just trying to put food on the table, they find out something is valuable, they want to sell it. The antiquities market is putting such value on artifacts that it encourages looting. Buying antiquities endorses looting, which supplies more artifacts and increases demand. Just don't.

It's not a good result. In fact, I have a personal experience with looting this past summer. The site I was working at was looted one night, and they took some very important artifacts that would have been extremely informative were we able to analyze them and excavate them properly. They could have contributed massively to our understanding of a tricky area. Now they can't do anything but look pretty, which is an extreme waste and one that I am still angry about.

Also, collectors don't always have good storage environments for the stolen artifacts they collect. They are stored in poor environments that hasten the degradation of the artifacts.

Finally, in many cases antiquities are the remains of ancestors of extant communities. Looting these sites is literally stealing from their ancestors and heritage. For Native Americans, the artifacts link important oral traditions with past places. Looting these is obviously disrespectful to their culture and damaging to their traditions.

Laws are in place to protect these remains. For the US, the Archaeological Resources Protection Act (1979) was enacted to protect archaeological sites from the incredible harm that looting does to a site just to obtain a few valuable items stripped of all their academic value. The Native American Graves Protection and Repatriation Act (NAGPRA) exists to apprise Native American groups of their heritage resources and provide a means by which they can request objects and remains to be returned to them.

Many other countries have antiquities legislation. In Israel, for example, which is the country where I have done the majority of my archaeological research over the past ten years. Israel Antiquities Law states that all antiquities within the State of Israel belong to the State, which allows them to regulate the excavation of the objects, ensuring proper recording and methods. Israel has licensed antiquities dealers, who are allowed to buy and sell antiquities under governmental regulation and must follow the conditions of their license.

I am not familiar with antiquities laws in other countries, but I have colleagues excavating in Central America (Guatemala, specifically) who have had to deal with their sites being damaged by looters.

I'm not an expert on the legal side of things, so a history of antiquities law is outside my wheelhouse, perhaps some other user can illuminate us on this.

In short, it's bad because it not only damages sites, but can damage the artifacts and destroys critical archaeological information.

A follow up question. How do current archeologists reconcile with the fact that those following them will likely view many of the results (not motives) of their efforts similarly to how we view looters today. That's probably harsh, but what you read about early archeology is a rather long list of "things that should have been left undone." As technology progresses I don't expect that will change much, though obviously some of that is a direct result of having started in the first place. I guess I don't know how I feel about it, and am curious how others more involved deal with the question.