If you're on Windows I really recommend the excellent Flash Develop. It's what I use daily at work as a flash developer, and I have access to both the Flex IDE and the plain Flash CS3.
FlashDevelop hooks up nicely with the Flex compiler which is available for free, it compiles both MXML (the "language" flex applications are written in) and Actionscript 3. It's a command line compiler so you can hook up any IDE you please to it.
This isn't exactly ideal for making animations, graphics and such, then you're better of with Flash CS3. But for plain coding this is way better, AND free.