Fractal Software
last updated 2/25/13
General Purpose

Xaos is a fractal zoomer.  It allows you to explore fractals by continuously zooming in and out.  It does this 'smoothly' (real time) so it looks like an animation.  It truly is beautiful to watch, but it you need  a fairly modern machine.  It has built in fractals that you can explore, while at the same time allows you to input your own equations.  It has various coloring and filter methods to make the fractal unique and visually stunning.  You can create beautiful works of art.  If you are willing to tinker with it.  It also supports Julia sets, if you are familiar with those.  You can save high res images, but only through a command prompt.  I keep hoping they add that feature to the GUI.  In addition, it lets you create and save fractal animations.  Also, the program has animated tutorials designed to teach you about fractals and provide an informative, yet understandably introduction to fractals.
Xaos Screenshot

Fractal Explorer
Fractal Explorer is a fractal generator.  It allows you to explore fractals, but it is not a continuous zoomer like Xaos.  It will zoom, but not smoothly.  What it does really well is custom fractals.  It has a large database of built in fractals and filtering methods.  It also allows more precise control of most all aspects of the fractal (from colors to filters).  It supports Julia sets and animations.  You can also input your own fractal equations, but this can be difficult.  My biggest complaint is lack of a help menu.  While there are some forums that can help, it can take time to find an answer.  Also note that the software hasn't been updated in 7 years.   Despite this, it is still a great tool for creating stunning pictures to hang in your office.
Fractal Explorer

Apophysis is a fractal flame generator.  I'll be honest, I haven't looked at it enough to know exactly how fractal flames are generated.  However, I do know it creates really cool images.  While being fractals in nature, they are more reminiscent of smoke and flame.  I only know about fractal flames because I run the Electric Sheep screen saver (see below).

Electric Sheep
Electric Sheep is a screen saver that displays continually evolving fractal flames.  It is made by the same guy that created the Aphophysis software above (Scott Draves).  The screen saver displays short animated fractals called 'sheep'  Each sheep is about 5 seconds long.  As these sheep are based on fractal equations, they take a while to render (compute).  Because of this, the work is distributed among the different computers running the screen saver.  That it, as you run the screen saver it generates frames for new sheep.  It uploads these frames to a server, the server combines the frames into a video, and then the screen saver downloads the finished video.  All of this happens transparently, so that you, the user, can just enjoy the show!  It is really a great screen saver and has application to both math and computer science.
Electric Sheep