While Jupiter having moons is what most people remember from what they learned of Galileo, the observations of Venus were the ones that actually changed the way that we look at the world.  Not only does Venus have phases… but the planet dramatically changes in size over the course of them.  You can see this for yourself with binoculars or a small telescope.

For more details on the process, including some very nifty diagrams that show how that picture proves it, wander over to science blogs.