Legend has it that Galileo dropped cannon balls from the top of the leaning tower (the campanile of the cathedral - see picture) to demonstrate his conclusion that the rate of falling is independent of the mass of an object. In fact, the experiment was conducted by one of his rivals, Giorgio Coressio, and was designed to refute Galileo's claims by demonstrating that heavy (massive) objects fell faster than less massive ones!

(Pictures from M. A. Sullivan http://www.bluffton.edu/~sullivanm/pisa/pisacathedral.html) and http://web.kyoto-inet.or.jp/org/orion/eng/hst/romanesq/pisa.html)

There is a legend that his first thoughts about the pendulum occurred as he watched a hanging lamp swing in the Cathedral at Pisa. The only problem is that the hanging lanterns were not installed until a few years after Galileo's first proposal for use of a pendulum to keep time (timekeeping was a major issue in the physics experiments he was conducting, so he would have been thinking about the problem seriously rather than idly while in church).