Looting art has a 3000 year history, according to Stephanie Goldfarb in Lessons in Looting.
According to Goldfarb, the first known looting occured in 1158 BC, when the conquering Elamites seized an Akkadian victory stele. The Romans glorified pillaging as a symbol of imperial splendor, but the Middle Ages saw pillaging revert to mere piracy. Napoleon revived the Roman tradition, while the Nazis, in the 20th century, turned pillaging into some sort of fetish. The Iraq War has seen all sorts of looting going on.
Regrettably, Goldfarb overlooks Indiana Jones.
Nevertheless, for a grand overview of this ancient tradition, read her article.