A historic case of extraterritoriality was the seizure of the railways of Nicaragua by Brown Brothers Harriman, a U.S. banking firm. Under the Knox-Castrillo Treaty of 1911 these railroads became legally part of the State of Maine, according to former president of Guatemala, Juan José Arévalo, in his book The Shark and the Sardines (Lyle Stuart, New York, 1961), pp. 210–220.
That's from the Wikipedia entry on extraterritoriality, a concept which none of you seem to have mentioned yesterday, at least last I looked. It's an old idea and here is Shih Shun Liu's seminal work Extraterritoriality: Its Rise and Decline. Here is a map of the Shanghai concessions and here are other Chinese ports. Liu describes Martens's Das Consularwesen
und die Consularjurisdiction im Orient as "indispensable". Many applications of the idea originate with the Crusades. Here is the Italian version of the concept.
I would count Puerto Rico, although it does not quite fit the formal definition, as a relatively successful application of the concept; the Panama Canal zone was another example. It is harder to find good examples with a more recent origin and it is unlikely the idea will be applied, say, to either Kaliningrad or the Kurdish part of Iraq. Here are comments from Will Wilkinson.
The U.S. Senate, by the way, did not ratify the Knox-Castrillo treaty.