The Trabant doesn't get a lot of respect in Europe, for obvious reasons, but it's definitely an unusual collector piece, especially in the USA. The convertible Tramp variant was built for the East German military and border guards (green for military and tan for border guards) and is even more rarely seen. This one, the 601F border guard model, is located in Birmingham, MI, and is for sale on eBay.
article on The Auto Channel from March 2005 that featured this exact car and it's present seller. A previous Trabant owner, he found this car for sale by a collector in Ohio and bought it with 7,000 miles. Turned out to be just 700, and it's now up to 1,200 miles (2,000kms). The owner said he didn't drive it often, just around town and at least once on the Woodward Dream Cruise. He appears to be knowledgeable about the car and has stored it indoors, kept it up nicely, and has the full top, windows, tools, original upholstery (under those seat covers) and an English repair manual. At the time the 2005 article was written it drove very nicely. I like the "DDR" country sticker.
here and here, both with reserves. Can't help but think he might get a better response to the auction if he included the picture at the top of this page from the Auto Channel article and some more information about the car.
Click on this picture to see a military-green Tramp on duty at the Inner German Border in 1982:
Now for some Trabant Jokes:
How do you double the value of a Trabant? Fill up the tank!
An East German driver pulled into a service station and asked, "Can I get a windshield wiper blade for this Trabi?" The mechanic looked the car over for a long time and finally said, "Okay, it's a trade!
Source links: Auction 1, Auction 2, The Auto Channel article, Trabant Wiki, border picture
UPDATE: Both auctions ended at $2,550, r.n.m.