Yep, the French and the British are still arguing about who shot the nose off the Sphinx during the Napoleonic wars. Military types don't generally blow up iconic buildings for fun, they do it for propaganda purposes, eg Shi'a mosques in Northern Iraq are currently getting pounded into dust by the Sunni extremists. Irregular forces are more inclined to go for iconic building to demonstrate their power, eg: twin towers, UK parliament, etc.
The worst case of heritage destruction I can recall recently was on the 3rd day of the Iraq war when the US sacked the entire public service and then sat on their hands while the locals went on a looting spree. It was an extremely foolish decision that backfired badly, no cops, no ambulance, no garbage collection, no school, etc. After the looting rampage was over the US had well and truly lost the "hearts and minds" battle with ordinary Iraqi's.