GIMP High-end photo editing and drawing package that has often been compared to Photoshop. It usually wins on price, but the Adobe product still has some exclusive features. If you're familiar with Photoshop but want to save on monthly fees, a fork that emulates its interface is available here: GIMPshop
 Dia Diagraming tool for flowcharts, network schematics, UML diagrams, and data modeling. Includes LOTS of pre-made objects.  Can read and write Visio VDX files and exports to other formats like EPS, SVG, DXF, and WMF. Similar to Visio, but with a more user-friendly interface. In spite of being a “sub 1.0” product (and a semi-inactive project), it is pretty stable at version 0.97.  Lack of development may be due to LibreOffice's "Draw" being pretty good too.
 Blender 3D modeling package that includes many professional rendering and animation features. Every function has a keyboard shortcut that makes Blender (eventually) easy to use. Not exactly easy to learn, but there’s plenty of training material available on-line. Several impressive videos made with Blender are also available. Download a full-length movie here.
 Hugin A “digital stitcher” that lets you join multiple photographs into larger panoramas or posters. Actually a very nice front end for a set of command-line tools. Simple if you use the defaults, really complicated if you don’t. Although highly capable, it’s one of very few free stitching utilities available.
 IrfanView Can view pretty much any graphic format and even a few video formats.  It also includes a bunch of editing options like color effects, cropping, resizing, negative, etc. Only free for non-commercial use, but it's too universally useful to ignore - and it's probably worth at least the $12 asking price.
 MicroDicom  When you get an X-ray or MRI disk from a radiologist they usually include an image viewer that won't work if you copy the disk.  This is an alternate viewer that lets you view as many copies as you care to make. As of 2017, there will be a fee for commercial use.  However, that doesn't affect the rest of us - and frankly, this indicates how good it is (that doctors and radiologists are interested in licensing it).