To help game developers with some of the common and complex programming tasks associated with developing Flash games, some developers have created game engines and frameworks to do a lot of the heavy lifting. Here are some of the common ones. Also be sure to read Adobe evangelist Tomas Krcha's overview of Flash gaming engines.
Adobe Stage 3D
Stage3D is the native GPU rendering pipeline developed by Adobe that allows your game to deliver blazing fast hardware accelerated 2D and 3D graphics to desktop browsers, mobile devices (iOS and Android apps), and TVs.
Flash game engines
The Citrus Engine is a professional-grade Flash game engine built with diversity, speed, and scalability in mind. The Citrus Engine was built to allow designers and developers to quickly and easily create Flash games without worrying about architecture.
A revolution in Flash game production. An amazing new way for man to interface with machine. The beginning of a new tomorrow. Never before has the world witnessed such a collection of AS3 files.
The Smash Framework is an industrial strength, Open Source Flash game framework that is designed for a new generation of games. Created by the team who brought you PushButton Engine, the Smash Framework makes it easy to bring together great existing libraries and components for building games using Flash technology.
TheoWorlds Builder SDK v2 is a kit that will help you develop online virtual worlds much faster, without starting from scratch. At its core it contains our original Theo Isometric Engine™ that lets you create pseudo-3D maps, place on them objects and characters, and organize the interaction between them.
Flash and web physics engines
Get a grasp on the importance of including physics in your game development in Samuel Rivello's overview article and then check out the engines below.