The original bridge was built by the Romans as a bridge of boats and this was replaced by various wooden bridges that were in use until 1176, when a stone bridge was built on the site.
The stone bridge was in use for over 600 years and became one of the wonders of the medieval world as it spanned what was at the time a fierce tidal river. The bridge had houses (up to seven floors high), shops and a church on it, similar to the Ponte Vecchio in Florence.
The stone bridge was replaced in 1831 by a granite bridge as it was becoming a hazard to boats navigating the river. This bridge was in turn replaced by the present, less spectacular bridge which was opened in 1973, and the granite bridge was reconstructed in Arizona, USA. (Some people believe that the Americans who bought it thought it was Tower Bridge.)
You can see London bridge on the cultural walk and bridges walk.