I draw my sprites in Paint.NET. It is a very useful program, and is meant to be a "free version of Photoshop". It really does have most of Photoshop's features.
Boopaloo uses Flash to draw, but I'm afraid it's not free. Or is it just me?
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Another approach to try is to draw on paper, then scan or photograph the image and clean it up with Photoshop Elements, Paint.Net, or GIMP.
Since I don't draw well (and I find a mouse almost impossible to draw with), I often use a digital camera to create my sprites (like for the MasterMind game: http://scratch.mit.edu/projects/kevin_karplus/12236
I do have to do a lot of touchup to get the images to be the right size and with the background removed , but that is easier for me than drawing.
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GIMP is free. I've never tried installing it, so I don't know how much hassle that is.
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I tried Google Sketchup, it's fun but made for modeling, not drawing.
And yes, GIMP is free, but it doesn't have as much functions as Paint.NET has... what a pity it doesn't run on your comp.
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