I've checked out V's topic on software information (Very helpful, indeed), but I'm having trouble deciding which free 2D program to download. I'm looking for a program that would support transparency, allows animation, and be able to create/edit textures. (Like Alias Sketchbook, but I don't have the money to buy the real stuff, and I don't like trial versions because I want something that can go with me for a length of time) Thanks!

Use The GIMP, you won't be disappointed.

If you want it to be free then it's definately The GIMP that you're after. Make sure you download GAP if you want the animation package.
Windows installers (if you don't want to mess about with the source) are here...
http://www2.arnes.si/~sopjsimo/gimp/stable.html

Cinepaint would be another option, based on the Gimp, but with HDR, animation support and flipbook (included, no need to download GAP). And it's faster with large images compared to the Gimp. (I also like the interface better, but that's just my opinion...)

I like the GIMP. It's interface is a little odd, but as you use it more and more you'll find you prefer it to anything else.

I recommend Graphics gale!!

Its quite good for what it is..