Okay, technically it's "just" a long since abandoned city, but as a deliberate assault on the memory of mankind it's really disgusting: ISIL claims to be bulldozing the ruins of the ancient Assyrian capital of Nimrud (one of a couple of cities that served as capital during the course of the thousand-yar long history of ancient Assyria) and preparing to destroy the city gate of Nineveh nearby. Picture if anyone would flatten the ruins of Troy or parts of Pompeii and you'll get the idea.
There are dozens of other first-rank archaeological sites in the area either controlled by ISIL or risking to come under their hands (including Babylon), and many of these, like Nimrud, were still being excavated before the Iraq war and could yield more important finds. One such site is Dura-Europos, near the former Syrian/Iraqi border and deep in ISIL territory, a city where the oldest Christian church ever recovered was found in the 1930s, together with a Jewish synagogue nearby, both of them from around 230 AD and with unique paintings and art (the church paintings were long since moved to Damascus, not the safest place either...). This is just very sordid, and the attacks on such places are also a direct assault on Assyrians as a people.