There are a handful of powerful and versatile generative art tools currently available:
Processing

Processing is an open source programming language and environment for people who want to program images, animation, and interactions. It is used by students, artists, designers, researchers, and hobbyists for learning, prototyping, and production. It is created to teach fundamentals of computer programming within a visual context and to serve as a software sketchbook and professional production tool.
VVVV

vvvv is a toolkit for real time video synthesis. It is designed to facilitate the handling of large media environments with physical interfaces, real-time motion graphics, audio and video that can interact with many users simultaneously.
vvvv uses a visual programming interface. Therefore it provides a graphical programming language for easy prototyping and development.
vvvv is real time. where many other languages have distinct modes for building and running programs, vvvv only has one mode - runtime.
Flash

Flash is the current go-to for anything on the web that requires animation and a high level of interactivity.
Quartz Composer

Popular among Mac developers and VJs, Quartz Composer is the simplest application for creating still as well interactive motion graphics. It uses a node-based sequencing visual programming language that takes advantage of the Open GL, JavaScript, Core Image and Core Video devices and other technologies built into Mac OS X. It’s intended for non-programmers and is used by developers to construct user interfaces in conjunction with Cocao and other developer tools bundled in Xcode. It’s also used to create iTunes Music Visualizers.
NodeBox

NodeBox is similar to Processing and OpenFrameworks with the only major difference being the programming language used, which is Python.
eMotion

eMotion is a new free application which can generate real-time as well as offset graphics. It has an awesome text and particle engine which is driven by real-world physics. It is available only for Mac OS X.