ImageJ is a free, open source, platform independent, general purpose image processing package written by Wayne Rasband, National Institutes of Health, USA. Visit the ImageJ website to download the program.
There is also an astronomically oriented version of ImageJ called AstroImageJ, which can be downloaded here.
ImageJ provides an interface to integrate user-defined plugins. A wide variety of plugins can be downloaded from the plugins page on the website.
Here are some plugins that I have written for astronomical image processing.
There are also several other plugins that are very useful for astronomical images. Here is a list of the ones that I use most.
Archive of all plugins listed in West and Cameron, JRASC, December 2006