Flash, if implemented correctly, can be a real benefit to your site, but if executed badly, you could lose visitors pretty quickly. We've gathered 20+ tools to help you make the best use of this powerful tool. Feel free to add more resources in the comments.
Action Script Library - A collection of code snippets for use with ActionScript.
ActionScript.org Library - A collection of over 700 scripts for you to use, a large selection of tutorials and more.
Actionscript Physics Engine - A free 2D physics engine for Actionscript 3 from MIT.
ActionStep.org - An ActionScript 2.0 open source component framework for writing to the Flash player.
Aflax.org - An attempt to bring Ajax and Flash together.
Animation Package - An ActionScript library (Flash player 6 and above) with a focus on keeping file sizes down.
AS2lib.org - The AS2 library open source framework to work with Actionscript 2.
AS2Unit.org - An Actionscript 2 testing framework that lets you run repeatable tests on your classes.
AsFusion.com - A blog written by two developers about merging ColdFusion and Flash and how they can work together.
DontClickIt.com - An experimenting in using Flash to make a clickless interface.
FFiles.com - A large collection of examples of Flash movies that you can view, rate and comment on. You can also submit your own for review.
Flalog.com - Tips, tricks, and tutorials for Flash and ActionScript.
FlashGuru.co.uk - A collection of articles, tutorials and extensions for Flash.
FlashKit.com - Code snippets, reviews, links, over 1,000 tutorials.
Flashtica.com - A designer-oriented site with open source scripts and links to lots of resources.
FlashVillage.com - Free Flash and Logo templates, forums, and more, registration required.
GoToAndLearn.com - A site with very in-depth video tutorials on various aspects of Flash.
Jim's Flash Bestiary - A collection of small Flash movies with accompanying source code to learn from.
Kirupa.com Tutorials - An extensive collection of tutorials on just about every conceivable aspect of Flash.
OneFlex.org Codes - A site for people to post and share code snippets for ActionScript and MXML.
OSFlash.org - A home for open source Flash projects that any registered member can contribute to.
Smart Webby Flash Tutorials - A collection of tutorials for Flash for beginner to advanced developers.
The Fuse Kit - A compact animation kit for Flash, more for everyday use than making full animations.
Tile Based Games Tutorials - Tutorials to learn how to create tile based games using Flash.
TutorialOutpost Flash Lessons - A huge collection of tutorials on many aspects of the Flash program. (via)