These are all very cute and sentimental reasons for keeping pennies in circulation, but the facts are they cost our government (which in turn costs the PEOPLE) millions and millions of dollars a year, they clog up banks, and we'd all be better
These are all very cute and sentimental reasons for keeping pennies in circulation, but the facts are they cost our government (which in turn costs the PEOPLE) millions and millions of dollars a year, they clog up banks, and we'd all be better off in the long run with a more streamlined money system.
In the long term getting rid of pennies will SAVE the American public, not cost us.
Paper and coin money is nearly already now a thing of the past. Let's start with the most expensive and least necessary coin: the penny.
It's about long term, growth driven, sustainable economics, not sentimentality.
Here's some excellent, evidenced based arguments for elimiating pennies, from Wikipedia, but the truth is available a lot of other places.
Arguments for elimination
Production at a loss — As of February 2011, it costs about 2.4 cents to mint a penny. In 2007, even the price of the raw materials it is made of exceeded the face value, so there was a risk that coins were illegally melted down for raw materials.
Lost productivity and opportunity cost of use — With the average wage in the U.S. being about $17 per hour in 2011, it takes about two seconds to earn one cent. Thus, it is not worthwhile for most people to deal with a penny. If it takes only two seconds extra for each transaction that uses a penny, the cost of time wasted in the U.S. is about $3.65 per person annually, about $1 billion for all America. Using a different calculation, economist Robert Whaples estimates a $300 million annual loss.
Limited utility — Pennies are not accepted by all vending machines or many toll booths, and pennies are generally not accepted in bulk; however, Illinois does accept pennies in its toll booths. In addition, people often do not use cents to pay at all; they may simply use larger denominations and get pennies in return. Pennies end up sitting in jars or are thrown away and are not in circulation. Economist Greg Mankiw says that "The purpose of the monetary system is to facilitate exchange, but... the penny no longer serves that purpose." 
Prices would not be higher — Research by Robert Whaples, an economics professor at Wake Forest University, using data on nearly 200,000 transactions from a multi-state convenience store chain shows that rounding would have virtually no effect. Consumers would gain a tiny amount – about 38/1520 (1/40) of a cent per transaction.
Historical precedents — There has never been a coin in circulation in the U.S. worth as little as the penny is worth today. Due to monetary inflation, as of 2007, a nickel is worth approximately what a penny was worth in 1972. When the United States discontinued the half-cent coin in 1857, it had a 2008-equivalent buying power of 11 cents. After 1857, the new smallest coin was the cent, which had a 2008-equivalent buying power of 26 cents. The nickel fell below that value in 1974; the dime (at 10 cents) fell below that value in 1980; the quarter (at 25 cents) fell below that value in 2007.
Hazards — The reduced-cost clad zinc penny, which has been produced since mid-1982, holds additional dangers when swallowed by children and others, unlike all previous U.S. coins. If the copper plating is breached, the penny quickly corrodes into a sharp-edged object, which is more likely to lodge in the digestive tract. Injury is more likely and furthermore, zinc and copper digested from the lodged pennies may be toxic. An 11 lb (5-kilogram) dog was fatally poisoned by swallowing two pennies.