Another option besides ActiveSWF is the recently announced Xamlon Pro Flash Edition. Xamlon is essentially an implementation of XAML the current version of Visual Studio. There's a version for Windows Forms, for Compact Framework and now for Flash. So basically, you can write your flash app with XAML and C#. Apparently, you can also code directly to the Flash format, bypassing the XAML layer entirely. I like the idea of using a managed component like Xamlon better than a COM based component.
My big issue with using Flash is that it's a totally seperate programming environment from the browser. Using VML in IE, you can manipulate the vector objects with javascript. In Flash, you may be doing one thing in the browser and something completely different in the flash movie. That's a pain in the behind.