I have traveled through a fair number of airports in my lifetime, but the EuroAirport is the strangest one I've ever been in. (I was there because it's the closest major airport to Freiburg, Germany, where I was working with Peter, my Many Tricks business partner).
The EuroAirport isn't strange due to layout or location or weird weather or anything. It's strange because the airport itself is split between two countries, even though it doesn't straddle a country border—it's 100% within the territory of France, but a portion of the airport "lies in" Switzerland.
This oddness is a result of the airport's development history: Basel, Switzerland wanted an airport, but lacked the space. France had the space near the town of Mulhouse, but lacked the money.
The two countries agreed to a joint development effort, starting just after World War II. The end result is an airport in France, paid for by Switzerland, and with portions of the airport physically being in Switzerland, despite the airport's location completely within France.
You can actually see this in Apple Maps, as seen in the above-right screenshot. Search on EuroAirport and you can see there's a set of country borders drawn on the airport itself; the outlined region belongs to Switzerland, even though the entirety of the airport lies in France. (Not shown is that the road leading from the airport to Basel is also Swiss property.)
The EuroAirport wikipedia page explains the multi-country layout quite well:
The airport building is split into two separate sections – Swiss and French. Though the whole airport is on French soil and under French jurisdiction, the Swiss authorities have the authority to apply Swiss laws regarding customs, medical services and police work in the Swiss section, including the customs road connecting Basel with the airport. However, French police are allowed to execute random checks in the Swiss section as well. With Switzerland joining the Schengen Treaty in March 2009, the air side was rearranged to include a Schengen and non-Schengen zone. Travellers departing from the airport into non-Schengen countries may receive either the Swiss or the French passport stamp, according to their entry choice.
If you set Apple Maps to satellite view, the split becomes even clearer; you can see that the terminal itself is divided right down the middle.
When I arrived, though, all of this was (mostly) invisible to me. I cleared customs, picked up my baggage, then exited to the main hall to look for Peter. Not seeing him, I sent a text, and he then asked me if I could come to the Swiss side of the airport. This was the first I'd heard of a different "side" of the airport, and I couldn't see what he was talking about—there are no signs that I could see indicating which country I was in, nor where the other one might be.
A few minutes later, Peter appeared, having walked through a one-way door in a dividing wall in the middle of the Terminal. As it turns out, this wall is what separates the two countries within the terminal. As Peter had come through a one-way door, though, we weren't sure how to get back. It turns out that the two sides aren't really all that separate: you just need to go upstairs, cross over, then come back down.
Which is what we did to then exit the airport, and drive off to Germany—meaning that I'd visited three countries within the span of about 30 minutes…and two of those were within one airport building. Weird but true.