Paint. net
According to it's website, it was engineered by undergraduates with help from Microsoft and was intended to replace MSPaint. Looks rather appealing and is still being updated regularly. With this one, you can use plugins, like Photoshop which is rather cool in my opinion.  

VCW VicMan's Photo Editor
Originally the Pro version was sold and the freeware version was only for enticement, but until recently, the pro version is also free to download. Has special effects, can draw on them, fix your photos, and more.  

Picasa 3
Google's own photo editing software. Here you can edit, organize, and even upload it to the internet. As a huge plus (in my opinion anyway), they do provide a tutorial system if you are new to it or to any photo editing software.
 

You might even be able to find some online that you don't have to download. In order to use this, I would HIGHLY suggest you have decent internet (no dialup- it would be too painful to wait for it and it might even crash);  

Gif Works
I've used this once or twice. Not too bad. But this was awhile ago when I used it. Great for creating gif images (moving images). Very basic.

Sumo Paint 1.0
Set up much like Adobe Photoshop, this online program is rather simple and easy to use. Has all your basics such as layers, swatches, shaping, color changing tools, and such. If you're interested in trying to understand Photoshop, or simply just wanting to edit an image on the go, this one would be perfect for you.

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If you have a suggestion or have heard of one that you think would be good to add to this... I would love to hear about it. All you have to do is send me a message. These are only a few of what's out there!