The one-cent coin costs more to make than it is worth, and its value is so low it is essentially useless. See http://en.wikipedia.org/wiki/Penny_debate_in_the_United_States. The "historical precedents" argument gives good reason to consider eliminating the nickel, and possibly the dime, as well.
Prices and credit card transactions could still be allowed to occur in cents, but cash transactions would be rounded. New coins (dollar, 50c, maybe 1/8 dollar?) could be introduced to appease the zinc and copper industries that benefit from the existence of the current coins, and keep Pres. Lincoln on coins.
I analyzed my 2010 expenses (~$75k) to see the effect of eliminating the coins, and it was in the noise.
Stop wasting taxpayer dollars making worthless coins.