Essentially all the software I use is free (legally!), and most of it is also open source. These pieces of software are what I would recommend if you ever have to do your own graphics editing work, especially on a tight budget.
Blender is a top quality free and open source 3D modelling, animating, texturing and rendering masterpiece. All 3D work and animation appearing on this site is produced in Blender; it is a very full featured program which rivals many top commercial 3D software.
The GIMP is the free and open source Photoshop. It is a bit of a monster and is not 100% user friendly but is very powerful with a huge range of filetype support and the potential for scripting.
Hugin is a very specialised piece of free and open source software used for combining multiple photographs into panoramas and HDR images. Although specialised it is an indispensible tool for photographers who want to do more than point and shoot.
Paint.NET is a free windows-only paint program. It is far simpler than The GIMP or Photoshop but is streamlined and very easy to use. Almost every image I make goes through Paint.NET for cropping and basic colour correction.
Inkscape is the free and open source vector graphics program. It is a truly excellent piece of software and the perfect tool for line drawings and assembling figures. Importantly it has extensive support for svg, the web standard for vector graphics.
Creature House Expression 3.0 is an old version of what is now Microsoft Expression Design available for free in the depths of Microsoft's website. It is a powerful and intuative piece of vector graphics software and I would recommend it (or its commercial follow-ups) as a more easy to use version of Illustrator.
VLC Media player is a free and open source media player which can play almost any file you throw at it. It also happens to have great transcoding tools (based on ffmpeg) and is my solution to all video transcoding nightmares.
ImageJ is a free and open source answer to scientific image processing. It fully supports (via plugins) essentially all microscopy image file formats, includes extensive advanced processing tools (eg. deconvolution), tools for quantitation and analysis and has a powerful scripting/macro language. Don't use the software that came with your microscope or camera, ImageJ will be better.
Python, a free and open source scripting language, is my choice for all general scripting tasks.
And last but not least, PHP, the free and open source server-side scripting language which has made this website and all its clever features possible without driving me totally insane.