A whole lot of this will depend on what you do, and your workflow, but maybe that's obvious.
I've got Pixelmator on an old Mac at home and it seemed okay for what it is. I've messed with Gimp and Paint.net on the free side of things. I've barely touched Elements, Corel, and recent versions of Paintshop.
These all may be fine programs on their own. The problems that I have run into (and have had co-workers run into when they didn't have a PS license) is that nothing I have found is 100 percent compatible with existing PS files. Sometimes it's text layers. Sometimes it's vector shapes or masks, or something else. It gets to the point where it's not worth it for me, at least not on a professional level.
If you work in a bubble and don't have to exchange layered files with clients/subcontractors/etc., there is probably something else you can use. If you're not in a bubble, you have to be careful.