Depends on the make and model of the frame. There are differences between English and Italian threading directions, and some Japanese-made frames will be English, some Japanese. Look for any markings on the exterior of the BB cups, as well as the spindle. I have a Fuji bike that had a Shimano 36x24t fixed cup, which is an Italian threaded model...

So look closely, take some notes, do some research before you wear yourself out cranking in the wrong direction.

Also, sometimes the cup has been installed super tight because the threads have become super gunked up, and there's only one thing that will get the cup out - a torch. If you really HAVE to get it out, perhaps as part of a repaint/restore, then break out the torch (or go to your friend who has a welding torch) and head up the cup for a couple seconds. It will cause the threads to give a little bit, allowing you to hopefully get the cup out (Source: personal experience. Worked fine for me.).