A penny saved is not worth the effort
If not for the superstition that a picking up a penny conveys good luck, any such coin dropped on the sidewalk would stay there until it was swept away along with other debris.
Adages involving the penny date back to when the coin was more than just a nuisance.
A "penny for your thoughts" was never a highly lucrative offer, but it wasn't an insult. The penny arcade was a place where brief entertainment could be purchased for one cent and penny candy referred to a variety of sweets sold one for a cent, or in some cases, two or three for a cent. The term "penny stocks" always was an exaggeration of the cheapness of certain stock offerings.
We can't think of anything that is available for a penny these days and it is long past time to phase out the coin as a nuisance. An argument could be made to phase out the nickel but that would not be practical without phasing out quarters. To have a system of allowing pricing in increments of 10 cents or 25 cents but not 5 cents would be confusing, and to eliminate the quarter, which is the most popular coin for vending machines, would be problematic.
Some people claim that the penny is necessary to pay sales tax, but it is not. To pay the exact amount of tax there would need to be a hundreth of a cent coin. Sales tax is rounded and it could be rounded to the nearest nickel if there were no pennies.
Some people fear that eliminating the penny would be inflationary. They figure that something that costs $1.99, for example, would become $2. Actually, since the psychological effect of being under $2 is the goal of marketers, the price would likely be $1.95 without the availability of pennies. Even if the price was reduced four cents once for every four times it was raised a penny, consumers would see no inflationary effect.
In the long run, there would not be much difference one way or the other, with retailers aiming for a certain percentage of markup when averaged among their total products offered.
There would need to be a sufficient time between the time customers would no longer be required to use pennies for a purchase and the time merchants would no longer be required to accept pennies for a purchase. Financial institutions could be required to accept pennies for a longer period and the federal government could be required to buy pennies from financial institution for an even longer period.
The cost to produce pennies must be a high percentage of their value. It would make good policy sense to eliminate them from our monetary system.