Baarle-Hertog: Baarle-Hertog borders the Netherlands – but, because of its unique history of political division, the town is sort of marbled with competing national loyalties. In other words, pockets of the town are Dutch; most of the town is Belgian. You can thus wander from country to country on an afternoon stroll, as if island-hopping between sovereignties.
Being in a bit of a rush at the moment, I'll simply have to quote Wikipedia:
Baarle-Hertog is noted for its complicated borders with Baarle-Nassau in the Netherlands. In total it consists of 24 separate pieces of land. Apart from the main piece (called Zondereigen) located north of the Belgian town of Merksplas, there are twenty Belgian exclaves in the Netherlands and three other pieces on the Dutch-Belgian border. There are also seven Dutch exclaves within the Belgian exclaves. Six of them are located in the largest one and a seventh in the second-largest one. An eighth Dutch exclave lies in Zondereigen.The border is so complicated that there are some houses that are divided between the two countries. There was a time when according to Dutch laws restaurants had to close earlier. For some restaurants on the border it meant that the clients simply had to change their tables to the Belgian side.
Sarah Laitner, at the Financial Times, adds that "women are able to choose the nationality of their child depending on the location of the room in which they give birth."