Canada and Denmark have the politest ongoing dispute over a small island. Each country's navy has sailed out to the uninhabited rock, put up a flag, and left a bottle of booze for the opposing country's navy.
It started in 1984 when Denmark's minister of Greenland affairs put up a Danish flag at Hans Island and left a bottle of brandy and a note that read, "Welcome to the Danish island." In 2005, Canada's defense minister landed there and put up a Canadian flag. The next month, Denmark sent a warship, put up a Danish flag, and claimed that the Canadian flag had blown over.
Danish Ambassador Peter Taksøe-Jensen has said that the countries continue to visit the island, with Denmark leaving a bottle of schnapps and Canada leaving a bottle of Canadian Club whisky each time.