There are two other towers in Pisa that lean, but the only one that counts is the beautiful and elegant marble tower in the Campo dei Miracoli.
Originally the bell-tower of the neighbouring Duomo, construction began in 1173. Continuous settling of the building, constructed on sandy soil, meant that it took 200 years to complete, allowing for lengthy periods in which the building was allowed to 'rest'. Some say that the building was designed to lean, but this has been refuted, though it cannot be denied that the architects did not seem at all surprised by what happened. The Tower was closed from 1990 until 2001 for the completion of an elaborate stabilization project and it is once again open to visitors - on a strictly regulated basis.
(Climbing the tower requires a reservation based ticket for 15 Euro. Expect 45 minutes to 2 hour wait, but there is a lot to see while you wait.)