[Kamikaze Chinchilla]

Gimp is the poor man's version of Photoshop. While it doesn't have as many features as Photoshop does, it does have all the things for basic artwork with a bunch of extras. I wouldn't recommend it for beginners, but for people who are aspiring to migrate into Photoshop or are looking for a program that is similar to Photoshop, Gimp is what you're after.

OpenCanvas used to be one of the easier ones, but they did some updates in there that made it less convenient. If you can find the older versions, it will work excellent for basic artwork and is excellent for beginners.

PaintTool Sai is also one that is easy for beginner's. It's also used heavily by professionals in the illustration industry overseas. It gives you most of the basics without being overwhelming like Photoshop or Gimp. However, I've only used this for doing line-art as the lines appear cleaner and less shaky than with all the other programs I've used. I have used Photoshop for coloring since Photoshop has more coloring options in one package. Migrating an image to Gimp might also be good.

There's also a more basic version of Photoshop online: http://pixlr.com/editor/ . It works straight from your browser. I think is probably the easiest out of everything above, but I don't know how reliable it is or what the performance is like when the image gets to be large.