Actun Tunichil Muknal
In the main 'cathedral' there are literally Mayan pottery and other artifacts laying all over the place, with nothing to prevent someone from picking them up (or stepping on them if they aren't careful). Guides are only permitted to take small groups in, but there were a lot of groups in the cave at the same time. In ten years this place will either be closed down, damaged beyond repair, or roped off so you can't get near anything.