Perhaps because of Korea's undeniably horrific experiences during the 20th century, many Koreans seem to believe that their country has been uniquely victimized and invaded more than anywhere else on earth--well over 2,000 times if one counts every border clash and pirate raid, as some assiduous victimologists have done. Reputable professional historians dispute this quite vigorously, although everyone agrees about the terrible destruction wrought by the Hideyoshi invasions in the late 16th century and Mongol invasion during the early 13th century. My own strictly amateur assessment of the broader context follows.
In the global competition for the prize of "most invaded territory" in history, I suspect Korea would be eliminated in the early rounds, even within its favored "most invaded peninsula" division. The competition in the "most invaded steppe" division is far more brutal. Even within the Eurasian peninsula division, the Anatolian, Balkan, Italian, and Iberian peninsulas have certainly compiled far more impressive records than the Korean peninsula, especially if one includes coastal piracy. Sure, the Korean peninsula has been invaded more often than the Japanese archipelago over the last couple of millennia, but both are in the bush leagues in the global scheme of things. In the "most invaded archipelago" division, Japan would probably not even be invited to the tournament, despite its devastating defeat in World War II.
UPDATE: Even the hard-nosed Marmot was putting his money on Korea.