Could society function without currency?

Jimmy J asked:


We all base our lives around making these paper-wannabe bills, but is there a different way we could function? Would we set up personal trades like they did in small communities? No, because we have a large population. Could we set up a communist-type society where we trade with other countries for their resources with our resources and give out a sort of rationing that people would work for by harvesting our resources? What would that rationing be? For freedom, we’d have to be able to get whatever we wanted with our rations. But isn’t that currency?
Any ideas on a society without currency and how it would work with our massive populations?