Would capitalism without banks work? According to Merriam-Webster's dictionary, capitalism is "an economic system characterized by private or corporate ownership of capital goods, by investments that are determined by private decision, and by prices, production, and the distribution of goods that are determined mainly by competition in a free market." 

One could argue that banks are the engine which drive capitalism in today's world, since they are the institution which actually creates money through the lending of money at a rate of interest. However, there is nothing in the above definition of capitalism which indicates that banks are necessary for capitalism to thrive.

My question is what would happen if every country in the world were to make a law that would make it illegal to lend money at a positive rate of interest? Then of course, traditional banks would cease to exist. But would capitalism also cease to thrive? In other words, would people lose their incentive or ability to produce?
Under most capitalism-like systems, companies are funded in two ways.  One is debt with positive interest, the other is by selling equity to shareholders.  If you could effectively prohibit debt, then companies could conceivably adapt by switching to a 100% equity model, in which individuals would shift all of their interest-bearing savings into shares.  This would create various inefficiencies (and create a lot of problems for consumers who would be unable to obtain mortgages), but wouldn't fundamentally destroy the incentive to produce.