The most valuable US coin is the 1933 Saint-Gaudens Gold Double Eagle. In 2002 an example of this coin was sold at auction for 7.5 million dollars. At the time it was the most ever paid for any coin in the world.
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I believe the birch cent, the first pennies made in 1792
I don't think it is worth much. You might be offered 3 times the face value at most. Most coins after 1965 are worth less because the silver content in them is different. Coins prior to 1964 are worth about 10 times the face value at most because of the silver content. Many jewelers and companies are buying old coins nowadays. You can easily get a free estimate for your coins.
A 1907 Indian Head cent is the highest mintage of the series, retail values for circulated coins are $1.00-$3.00 for most coins.
Looking for someone to tell me what some old coins worth
The best thing to do is get a copy of "Red Book" a Guide of US coins, it has values for all US one cent coins.