Available on many platforms and agurably the most robost free alternative to Photoshop, GIMP has been a thriving image manipulation program since 1996. There may be a learning curve, but it's time well spent.

Official Site:
http://www.gimp.org/

Operating Systems:
GNU/Linux • Win • Mac OS X • FreeBSD • Solaris • AmigaOS 4 • & More

Learning GIMP:
http://docs.gimp.org/2.6/en/
http://www.gimp.org/tutorials/
http://www.ghuj.com/
http://gimp-tutorials.net/

Mentored by Microsoft and first released in 2004, Paint.NET is now another powerful competitor that's a free alternative to Adobe Photoshop. While the features are similar to GIMP, this program seems to be most intuitive for Windows users, but is available only for Windows users albiet in multiple languages.

Official Site:
http://www.getpaint.net/

Operating System:
Win

With layers, an array of filters and even 3D, the free version of this program is better than the paid of some other Cloud based graphics editors. The responsiveness and feature richness is highly impressive. If you like it enough, the paid version allows you to keep a local copy of the Sump Paint (no internet needed to use it). This little sample image below was made in about 5 minutes which isn't bad, considering the inexperience of the user.

Official Site:
http://www.sumopaint.com/home/

Learning Sumo Paint:
http://www.sumopaint.com/tutorials/

This free web based graphics editor is especially good for photographers. Many of the presets and controls will be found useful for photographers. Navigation is a little less intuitive than some and there are less tutorials available to learn, but it's figured out after just a few minutes still. It's espcially good for those looking for easy effects to apply to a photo, yet offerrs more advanced tools for when you're ready.

Official Site:
http://www.picnik.com/

Learning Picnick:
http://www.flickr.com/photos/bitnik/galleries/72157625....

The high interoperability with Splashup and other media sites is a major highlight. Able to connect to Flickr, Facebook, Picasa, SmigMug, Photobucket and more you can pull your web images and save back. I stress "web images" because this software does not play well with high res images. It has basic editing features, does not take advantage of keyboard shortcuts and while working well, its filters are limited.

To get the effect I got with this Spashup example, I used filters to make it Grayscale, then Enrich. At the size of the file, font would not show up, so I added the watermark in Photoshop.

Official site:
http://splashup.com/

Learning Splashup:
USCA.edu Student Page
YouTube Tutorials

Very similar to Adobe® Illustrator® in its wide range of features, this tool is really powerful.

The photo above is an image created in Inkscape. You can click on it to view a larger version of it.

Official Site:
http://inkscape.org/

Operating Systems:
Linux • Mac • Win

Learning Inkscape:
http://wiki.inkscape.org/wiki/index.php/Inkscape

Artwork is part of an Office Suite called "KOffice" which includes software for word processing, spreadsheets, presentations and vector graphics creation (Artwork).

While it's available on Windows and Mac OS X, it appears its focus is on Linux and FreeBSD.

Official Site:
http://www.koffice.org/artwork/

Operating Systems:
FreeBSD • Linux • Mac • Win