Hey there! Graphics Gale is currently free and a program that many pixel artists seem to like.
GIMP can also produce pixel art and there is also Paint.net that can be downloaded as well.
MSPaint that comes with windows can also do it, but I'm not sure if you can get transparent backgrounds with that one, I don't really use it.
I actually prefer Pyxel Edit myself, I find it to be the most user friendly and convenient. I hear the free version is buggy but it is available. The full program is just 9USD at the moment. Its still in beta, but has some great features that help build tilesets more easily, has onion skin for animations, and recently had an update that lets you save a default or preset palette that you prefer. I know you're looking for free programs right now, but its pretty affordable in my opinion and if you decide you really like doing pixel art maybe it could be something to consider in the future.
Wishing you the best of luck, and I hope you have a blast!