Flash and AIR Debugger, Open Source
For my Flash projects, I've started using a debugger called MonsterDebugger which allows you to debug right from the browser, or if you're creating an AIR app, right from the app it self. This is great because the default Flash debugger doesn't allow you to do much if your app is embedded in a CMS (like Drupal or Joomla), or relies on some kind of server side language for input.
Unlike many other debuggers, MonsterDebugger also also allows you to see all available methods and properties in an application, and CHANGE them on the fly, in real time! You can see the results of your changes, without closing or refreshing your app. This to me is a huge plus!
Also, if you're compiling with an application like FlashDevelop, which doesn't have as many features in it's debugger, you'll have a much more robust feature set combining it with MonsterDebugger. And the other thing is, like FlashDevelop, MonsterDebugger is free and open source. :-)