"Rare" gets bandied about a lot. As someone else pointed out already, just do a Craig's List search for "rare" and then enjoy the ride. That said, I tend to think of "rare" as having several levels of distinction. Here are a few...

Rare: ca. 1989 Freschi Supreme Super Cromo. I've never seen another in person, and only one or two photos of other examples.




Rare and unusual: ca. 1980's Houdaille. Finding any information beyond a paragraph or so was tough.




Rare and unusual - but not necessarily desirable: Brillant folding bike.




Rare and probably never see another: Brewster Pneumatic Safety Bicycle, ca. 1895-96