(This is a list question with many possible answers. Mirroring the meta proposal for references I'm making this is a community wiki - please feel free to edit to add more examples.)
Abbey of Monte Cassino, Italy - SJuan76
Reims Cathedral, France - gdir
Various actions on the Eastern Front of WWII - Fedor Nazarov
Warsaw endured many, many such acts of destruction by the German occupers during World War II. For example, the Great Synagogue, the Chopin Memorial, and the Royal Palace were destroyed early in the occupation. After the Warsaw Uprising was suppressed in 1944, the Germans systematically demolished the city (including its Old Town) while the Soviets watched from the other side of the river. (user31389 and Spencer)
Mỹ Sơn Temples and the Imperial City of Huế, Vietnam - ssdecontrol
The Gwanghwamun and Yŏngmyŏng Temple, Korea - user5001
The destruction of the National Library of Bosnia and Herzegovina by Serbian forces during the Bosnian War in 1992.
(See the linked non-wiki answers for details on each entry.)
