Of course, Alaska is the world's largest exclave, but Europe is full of enclaves, semi-enclaves, counter-enclaves, exclaves, semi-exclaves, counter-exclaves, and pene-exclaves: there's San Marino and Vatican City and Gibraltar, and scores of them in Belgium alone.
The true champion of exclavery has to be Baarle-Hertog, which is part of Belgium, but has a series of tiny exclaves surrounded by the Netherlands. There are 22 in total, and these are made even more insanely complicated by the fact the Netherlands commune of Baarle-Nassau has seven exclaves within Baarle-Hertog. In several instances, the border runs through people's houses - just google "Baarle-Hertog".
The following diagram may help to get your head around such territorial discontinuities. Please study it carefully as I'll be asking questions later.
You might as well start getting used to all these words, because Russia's exclave - well, semi-exclave, really, because it has one sea border! - of Kaliningrad could very soon become the next geopolitical flashpoint.
Want to see more of Königsberg? (I prefer its old name!) Click here.