The penny is no longer a useful part of the US coinage system. As of 2011, the production cost of a penny was 2.4 cents. Due to inflation, the value of the penny has become so minute that it can hardly pay for anything, even its own production cost.
Pennies have limited utility. They are not widely accepted in machines, toll booths, or in bulk.
In 1857, The mint stopped producing the half cent coin, which was worth what a dime is worth today. There were no resulting economic effects.
Pennies today no longer serve the purpose they did when they were introduced. It's time to retire the penny.