PixiEditor is a free, open source 2D graphics editor that you can use to create video game sprites, animations, pixel art, painting, and even vector art.
Synfig Studio is an open source 2D animation app that can be used to produce both vector-based cut-out animation and film-quality animation using bitmap artwork.
Blender is an all-in-one free and open source 3D modeling program that allows you to model, sculpt, rig, animate, run physics simulations, render, composite, and even draw and paint all in one application.
FireAlpaca is a free digital painting software designed for both Windows and Mac users, featuring regularly updated brushes, comic panels, animation tools, mesh transform, 3D perspective tool, and more.