When cooking soup, should I cover the pot or leave uncovered?

It completely depends on what you want out of your soup. Leaving the lid off will cause the soup to evaporate, leaving you with a thicker, more strongly-flavoured soup. Just uh, less of it. Leaving the soup with the lid off unattended can reduce it too much though so you want to be aware of what you're doing.

So in short - taste it and see what needs to happen to it. If you don't know, I'd lid it. You can always reduce later.