Steven shared a post arguing for the scrapping of the US dollar bill and one-cent coin. Canada scrapped the dollar bill ages ago but are still trucking along with the penny.
Of pennies, the author says "few rich countries have a coin so worthless", which I find a bit strange since all of Europe has a penny... I guess it's not technically "so worthless" since it's worth 1.5 US cents, but in relative terms it amounts to more or less the same thing. They also have a 2c coin, which is curious in the eyes of a North American.
Australia, though, got rid of its penny a while back and now rounds all prices to the nearest 5 cents. As a result, I recall seeing a guy with a Ferrari right smack in the middle of the Nullarbor, hundreds of kilometers from the next gas station, making sure to get the "perfect" pump that would give him his two cents of "free" rounded-off gasoline.
Interestingly, Europe (including the UK) and Australia both have 5,10,20,50 cent (or pence) coins instead of the 5,10,25 cent coins used in North America. When giving change, the North American system requires more coins in almost every case. Having a 2c coin gives Europe another edge here and dropping the one- and two-cent coins put Australia firmly in the lead for fewest coins required on average.
Of course the sub-five-cent coins are rarely used in Europe anyway because sales tax is already included in the prices. This means your €3.95 sandwich will get you 5 cents (one coin) in change while your $3.99+7% tax sandwich will put 73 cents (7 coins) in your pocket. Simply moving to include the tax in prices would significantly reduce demand for the US penny.