Before, I used mtPaint, though it doesn't really have good animation features. Very good for editing tiny paletted image files tho.
In one of the previous Humble Bundles, I got Pyxel, which is actually pretty damn good, particularly because it makes managing whole tilesets and various animations really easy. I really, really like the animation features, you can immediately see where where things go wrong and fix it in no time. It will export standard PNG files which just about all engines can handle just fine.
I'm well on way to make a game on Turbo Pascal 7.0 for MS-DOS. (None of that is technically sane. Please use a little bit more modern video game frameworks that can actually read modern image file formats, because you will save so many headaches that way.)
The Reddit thumbnail version without said orange spot, draft 1. Done in mtPaint in about 20 minutes, please shoot to pieces :3
I can tackle the vector version in the morning. My brain is slightly confused I'm still awake, it expected I would be asleep right no-ZZzzzzzz
I use a program called mtPaint small like paint but with better zoom and pixel grid features. It is designed for creating pixel art but it works great. Here it is.