Game Maker
Mark Overmars
There are many different 'free' or 'shareware' packages that you could spend your $15 (or 15 EUR) on, but if I had to recommend one, it would be GameMaker.
Note, though, that at the time of writing, GM is limited to 2D or isometric game development. 3D remains just out of reach, which means that it is not suitable for all budding game creators.
On the other hand, it offers a platform that is easy to use, with a drag and drop development interface which means that you do not need to get your hands dirty unless you really want to.
Support for GM is amazing, via two different magazines, a glut of tutorials, and more than 100 active sites devoted to it.
The author teaches game design (amongst other topics) at Utrecht University in the Netherlands. GM is freely downloadable, with a $15, 15 EUR registration fee that removes a splash screen for products that you wish to distribute.