We will always need some form of currency to trade for goods and service or the world would fall to ruins. How else would you trade amongst each other. In theory it's possible but would most likely lead to mass thievery and general anarchy.
We could return to our original ways o trade. You know, a fur coat for sugar and stuff. A sheep for a pig, that kinda stuff. Or we could make something else like... Marbles, our currency, like, 2green marbles would be forty bucks worth.