cmos chips for things like vending machines and such like use little programs on chips with no os. Close as you can get i spose to having no os. But it is still running operations so it's an os. Sort of like how long is a bit of string.
Well operating systems havent always been around, so I guess the question is can you create programs that for example only access maybe the keyboard and screen on an x86 processor without creating timesharing, drivers for other hardware etc. I understand that such programs would be tedious, but im sure theyre possible to write. you would probably have to learn every aspect of the processor architecture, the graphics card, how to load from a floppy disk (or cd?) etc.