I use XYplorer on Windows. It is heavily customizable, which has allowed me to turn it into the File Manager I always wanted. The free version has everything I need, the pro version adds some features like scriptability.

On Android, I am using X-plore (free again), which is also very innovative (it takes a bit to understand its design philosophy), customizable again, and very good. Only issue I see with it is that whenever it is running, battery drain is measurably higher. Thankfully it has an exit button in the GUI.

I'll add Clover (http://ejie.me) to this list. It slaps WebKit onto the stock Explorer, giving you tabs, bookmarks, and some nice keyboard shortcuts.

I use Far Manager (with plugins, e.g. Colorer and NetBox) on Windows (in ConEmu). Total Commander and other GUI based filemanagers are too far disconnected from command line, in my opinion.

On Windows there's Directory Opus which is really powerful, Total Commander is also really great. On OS X there's Pathfinder which is pretty good.

Directory Opus is great, but it is expensive. Last time I checked it was 70 dollars for one computer and that doesn't include "major" updates which seem to happen fairly frequently.

Funnily, Directory Opus got its beginning on Amiga.