A couple of candidates. For truly exotic historic vehicles, I nominate the German Rumpler. It looked like the cabin from a zeppelin, with an interior like a railroad parlor car, and was said to have been so aerodynamically efficient that when driven down a dirt road at high speed the only dust came from the tires. I saw one of these up close at a museum exhibit in Montreal a few years ago. Wonderfully bizarre. Rumpler was an aircraft designer, and although he didn't have modern technology, he managed to desing this thing with a drag coefficient hard to match even today.
http://www.design-classic-cars.de/rumpler/Rumpler-3.jpg
For even more exotic, try the Bugatti 57 aerolithe (Also sometimes identified as an Atalante, though not all Atalantes looked like this), which in pictures looks quite large, but was actually about the size of a VW beetle.
http://www.bugattipage.com/voitures/period2/57-at.jpg
Because the body was made of aluminum, and it was impossible to stamp the fenders and other parts in a single piece, they were made of two pieces, with a standing seam, riveted together. This is the car Captain Nemo might drive to the premiere of "City of Lost Children."
For less exotic, and something I've actually driven, I would nominate the 3-cylinder two-stroke "cornpopper" Saab 96. Here was a car that among other things regularly blew smoke rings at idle. In the engine compartment and under the seat were special little brackets to hold spare cans of oil. Because the transmission freewheeled (necessary because a two-stroke will starve for oil at closed throttle if you don't drop it to idle), you could downshift without the clutch. When approaching a corner under power, the horrendous understeer would push you straight through as if the steering were disconnected, until you let off the gas, whereupon it would pop around the corner as if it had been pulled on a string. Very stable in its own peculiar way, and easy to stop unless you overdid it, when the rear end would totally unload and the entire car would do a pirouette on its front wheels.
For really weird cars that never quite made it, how about Bucky Fuller's Dymaxion?
Some of my other favorites have already been named. Interestingly most are French.
