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.

For doing complex development with Flash, it can help to have a more powerful Actionscript editor than the built in Flash CS3 editor. I've been testing Flex Builder and FlashDevelop, both of which can export both Flash or Flex (Flex is Flash with a library of components built for making web applications). Both seem to have their pluses and minuses. FlashDevelop is free.