Galileo wasn't the first to do this. Flemish engineer/mathematician Simon Stevin (1548-1620) did the experiment. Even earlier, the 7th century Byzantine scholar John Philloponus (John the Grammarian) described the experiment in detail, in a manner which leaves no doubt that he had actually done it.
To make matters worse, Galileo probably didn't even do the experiment himself, at least he never claimed he did. No document of the University of Pisa mentions it, nor does any other independent source. The story was likely the invention of Vivani, Galileo's pupil and biographer. Galileo did describe such an experiment, and used it in arguing against Aristotelian mechanics. The myth still shows up in textbooks. It should have died when Lane Cooper demolished it in a pahmphet titled Aristotle, Galileo, and the Tower of Pisa (Ithica, 1935; Kennakat Press, 1972).
This is often repeated in various forms. Sometimes the questioner is said to be "a woman", sometimes "William Gladstone, then Chancellor of the Exchequer", and sometimes it's merely "The Prime Minister". Seldom is a date given, and when given, there's no consistency from one version to another. The great differences between versions of this fable should make one suspicious of its truth. Such an incident would surely have been reported in newspapers. But there's no documentation for it. See The Urban Legends Reference Page, Quotes. Also see the next item.
Franklin did observe the first balloon ascension on Nov 21, 1783 staged by the Montgolfier Brothers. Franklin may even have said this, though there's no specific documentation. It was a common riposte of that time, and still is today. It's unlikely it is an original witicism of Franklin. Sometimes it's seen attributed to Thomas Edison, and no doubt he would have used it, too. I've even seen it attributed to Michael Faraday (see previous item). Why is it that lame platitudes are considered more important when attributed to a famous person? You can bet that if Franklin or Edison did use such a quip, they didn't say "As the great Leonardo da Vinci said when asked the use of one of his inventions...".
This multiply mistaken unfounded assertion has even crept into textbooks and physics lectures. Windowpanes in old houses have varying thickness due to the glass manufacturing process used, and were usually installed thicker side down.
First, the assertion that the panes are thicker at the bottom isn't quite true. Some old buildings have window panes thicker at the bottom, and when that is so, it was probably custom or preference on the part of the builder. Many old buildings have panes where the thick sides are oriented in various ways.
Second is the misleading assertion that glass is a liquid that flows slowly. There's some validity to this, for glass does sometimes flow, but so slowly and so little that in the time since the old glass was made, you'd not get anywhere near this much thickness difference, or even a noticable difference.
If the assertions were true, the amount of thickness observed in houses of the 18th century should be, on average much less than that observed in buildings of the 15th century. But that is not the case.
The thickness variation is observed in glass made by a process in which a layer of glass is flattented by rotation on a flat surface. The thickness varies from center to rim of the wheel. When cut into pieces, each piece has a thicker edge. A professional window-maker will usually choose to orient the thick edges the same way, for esthetic reasons. Also, we have an intuitive feeling that a solid object is more stable if its heavy side is down.
Modern glass for windowpanes is made by floating molten glass on a liquid surface, which produces a very flat surface, and very uniform thickness.
You can learn more about it at these links.
Ivars Peterson has a good account of this, with references, in Ivars Peterson's MathLand (3/29/97).
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