Flixel & FlashPunk
These are two flash libraries that will help you get up and running making flash games without needed to pay for the Adobe's commercial Flash suite. They're arguably better to work with for games than the messy IDE anyway. It's very difficult to recommend one over the other, and the developers of both are friends. Best I can say is that Flixel is more mature, there's a lot more games out there made with it. Flashpunk on the other hand has much better getting started documentation. Expect to spend some hours getting everything up and running your first time around.
- Flash Game Dojo - A great "getting started" site for new users of Flixel or Flashpunk run jointly by the makers of both libraries.