I haven't used AS3 so I'm not sure what file types you need but I use https://www.gimp.org. It supports quite a variety of export options and is 'reasonably' easy to use (sometimes it doesn't work the way I intuitively expect it to and it's a fuss to figure out how to get it working as I expect).

Paint.NET is also a decent free tool (http://www.getpaint.net/download.html)

Paint.Net is usually what I install to take over duties for Windows' in-box Paint. Its not a fancy program, its just a better Paint, and its free.

Gimp is a free Photoshop replacement, so its got things like layers and tons of photo manipulation tools. The interface of stock Gimp is good these days, but different than Photoshop. If you're at all familiar with Photoshop already, I know there was a fork of Gimp that was made specifically to mimic Photoshop's interface, but I forget the name of it and don't know if its maintained and up-to-date with standard Gimp.

Inkscape is a free program for creating vector-based art (like Adobe Illustrator, and as commonly used in Flash-based games) that's pretty good.

For creating low-resolution and/or low-color graphic assets I find that more specialized tools are better for me. Things like GraphicsGale or Tiled. Cosmigo ProMotion remains my favorite; its not free ($59 to buy in, $29 to upgrade to the next major version), but its well-worth the money. ProMotion is still fairly popular for 2D sprite games on mobile deviced and handheld consoles (though less-so with devices capable of high-color graphics in the newer ones) and was used to make Shovel Knight.

But there are a multitude of competitors free, cheap, and otherwise in any of these categories and even the paid ones have free trials. It never hurts to download and test drive them until you find the one you like.

Depending on what you need to do:

• Krita for painting, particularly with a tablet; very good with layers.
• Inkscape for vector art (including rendering images at any resolution you need for use as sprites and further editing)
• Gimp for low-resolution pixel art.
• Gimp and Paint.Net for generic less creative editing tasks. The main difference lies in plugins: both have plenty (ranging from half-assed experiments, to simple and practical, to refined workhorses), but Gimp also has G'MIC, which should be enough for everyone, while Paint.Net has a significantly advantage if you want to write custom plugins (.Net, and the Codelab plugin development environment, rather than Scheme or Python or C with an irksome API).
• Shoebox for various specific tasks.