Well, these microscopic examples (molecules), and small-scale examples (pulley-belts), and far-out, conjectured cosmological examples are all well and good, but as a Bostonian born and bred I am disappointed that you are all apparently too young to remember the amazing example of the famous Moebius subway line that was part of Boston's MTA (earning it the nickname "Moebius Transit Authority"). The details can be found in A. J. Deutsch's remarkable story, "A Subway Named Moebius":

http://www.iblist.com/book12352.htm

And it was made into a famous prize-winning movie called strangely enough "Moebius":

http://www.dm.unibo.it/bologna2000/mosquera.html

And there is also a famous ballad written about it. (See : http://www.stationreporter.net/boston.htm

Well, let me tell you of the story of a man named Charley on a tragic and fateful day. He put ten cents in his pocket, kissed his wife and family, went to ride on the M.T.A.

Chorus: Well, did he ever return? No, he never returned and his fate is still unknown. (What a pity! Poor ole Charlie. Shame and scandal. He may ride forever. Just like Paul Revere.) He may ride forever 'neath the streets of Boston. He's the man who never returned.

(See : http://www.stationreporter.net/boston.htm for the full lyrics)