In recent years the US has made anywhere from 5 to 14 billion cents* every year depending on demand, so that works out to 13.7 million to 38.4 million daily. These figures are of course just averages, because the amounts change every year.
(*) To be annoyingly technical, the answer should be "none" because the coins are really cents, but we all call 'em pennies anyway ...
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According to the US mint, 6015.2 million pennies were made in 2012.
6,000,000,000 pennies equals $60,000,000 (sixty million dollars). 6 billion is about half of the total number of pennies made each year - 13,000,000,000 - so you are unlikely to see that many at once.
The mintage data for US Lincoln cents dated 2001 is: 13,519,196,000 this includes Proof coins.
The answer will depend on which country's pennies the question is about. Many countries have pennies in their currency - including the US where a penny is a cent! Most of these coins are of different and so no answer is possible.
In 2011, the U.S. Mint produced 4,938,540,000 pennies.