Technically, this shouldn't still exist. Originally meant to be dismantled after the 1897 Tennessee Centenial Expo, the Nashville Parthenon was such a hit with the public it became a permanent attraction. Our friends at Oobject have some other great examples of temporary architecture with staying power.
The Museum of Science and Industry, Chicago
The Eiffel Tower
The Nashville Parthenon
The Palace of Fine Arts, San Francisco
The London Eye
The Young Vic Theatre, London