I took quite a few pictures of the traditional May Day cruising event in my home town. Here are some of the first ones i took, all the photos (300 images) can be found here: http://imgur.com/a/1N6Cy . Please excuse if I've misidentified some of the cars, feel free to correct me
Plymouth Duster/Dodge Dart
Dodge Monaco?
Dodge Challenger
Mid-50s Cadillac
Dodge Polara?
Chevrolet Camaro
Early Mustang
Another Camaro
Chrysler?
1958 Ford Fairlane
Early '60s Chevrolet being overtaken by a Porsche Panamera
1928 Ford Model AA (?) with a Saab 99 hiding behind it
Plymouth Road Runner?
Late '50s Plymouth Custom Suburban?
Early '70s (?) Mustang
Late '50s Cadillac
Late '60s-early '70s Cadillac
Chevrolet?
Freightliner truck followed by a six-door Mercedes W211 which unfortunately isn't very visible
I also saw a Chevrolet badged Daewoo Nexia today, it had some Eastern European plate. It was parked next to St Mary's Cathedral in Edinburgh but didn't take a picture.
Honda Elite in Fairfax in a wonderfully period-correct color scheme:
Old Ford F-250 ice cream truck outside the Smithsonian National Museum of American History in Washington, DC:
Old BMW 6-Series on Pennsylvania Avenue NW in Washington, DC:
Chevrolet motorhome converted into a food truck at Farragut Square in Washington, DC:
The local Aston Martin-Bentley-McLaren dealership in Tysons Corner. Somehow, Bentleys seem less special when seen en masse. The black Bentley Continental GT3-R in the first pic is noteworthy because I thought the GT3-R was only available in white (there is a white GT3-R inside the showroom):
And last, a car that never goes out of style, a Packard Twelve in Washington, DC:
I might be wrong, but I'd say it has to be related to gliding planes. Near my hometown, there was/is a very active gliding-club, too. When I was a kid, I often used to watch them, and IIRC, they used old clunkers just like the one you posted to recover the "ropes" that were dropped by the planes/gliders right after the starting-procedure.