Chesapeake Bay Bridge-Tunnel, Virginia USA: The Chesapeake Bay Bridge Tunnel is one of the eight bridge tunnel systems in the world. It is about 23miles long and combines both a bridge and a tunnel for passing through the Chesapeake Bay to connect with the metropolitan Hampton Roads, Virginia and other parts of the Northeast. More importantly, this tunnel was created to protect the U.S. Naval base in Norfolk during wartime. If the bridge was to be destroyed, it would not hamper the movement of the Navy and they would still get to where they need to be without the bridge.
London Bridge, Lake Havasu Arizona: This bridge poked my interest because of the rigor of building it. This is the bridge that made the song "London bridge is falling down" common. It was originally erected in London over the Thames River, but it became too small to accommodate all the demands put on it. The Bridge was eventually put up for auction and bought by Rober McCulloch, the founder of Lake Havasus City. Each brick was numbered one by one and it took 3 years to move the bridge piece by piece from London to Lake Havasus Arizona where the London Bridge now sits. If you never got a chance to see the London Bridge in London, you can now see it in Arizona.
Ponte Vecchio, Florence Italy: This Bridge is the oldest and most famous wholly stone built, closed, and segmental arch bridge in Europe. This bridge was home to a lot of medieval merchants and butchers, but now is occupied mostly by hawkers, souvenir shops and art shops.
The above are definitely not all the unconventional bridges in the world, they are representative of some of a whole and speak volume of what the minds of people can conceive and create. Now it's your turn to vote for the best bridge of the five in your comments.