Many collectors, like myself, started buying artifacts out of interest for a particular culture or type of item. As they become more educated collectors, they start to realize the damage that is being done to the historical record by looting. They become aware that a way to help curb looting is to only buy items with provenance. Unfortunately for many of us, it's too late. We already own unprovenanced items. So the question now becomes "What should I do with the items I already own?"
The answer is to start documenting them now. Write down anything you know about the item. Who did you buy it from? When? Where did that person get them from? (If you have that information) If you have done any restoration to the item, document that as well. Take pictures of the item and keep them with the paperwork. This will be the beginning of a provenance. Should you decide to sell the item, pass all this paperwork on to the buyer, and try to educate them of the importance of keeping and updating this paperwork.
The best advice I can give to anyone concerned about the destruction looting causes, and wanting to make sure their items were legally obtained is to educate yourselves. Familiarize yourself with the laws concerning the items you buy, and the laws of the countries you are buying from.
There is much more to being a responsible collector than just requiring provenance, for more information see here:
This is a Code of Ethics created by a group of responsible collectors belonging to the Yahoo forum Ancientartifacts. There was a lot of time and effort put into creating this, and if followed by the majority of collectors it could make a significant impact on the destruction caused by looting.