US cents minted since mid-1982 are zinc with only a thin layer of copper plating, so the answer is "not much".
The coin weighs 2.5 gm of which only 2.5% (0.025) is copper, so there's only 2.5 X 0.025 = .0625 grams of copper in the plating. At today's prices that amount of metal is worth about 4/100 of a cent!
OTOH if you're talking about older cents, they're made of a bronze alloy containing 95% copper, which makes the metal in them worth about 1.7¢ IF you could get enough of them together to make them worth melting ... and IF melting cents weren't illegal.
Bottom line: New cents - spend them. Old cents - check with a price guide, dealer, or collector to see if they might be worth more as collectibles. Many aren't, but some cents from the 1930s and earlier can be worth a premium. In any case, you have to know the coins' specific dates, conditions, and mint marks to determine their possible value as collectibles.
About $3
It's worth 2 cents for the copper.
About 2 cents.
It's worth about two cents for the copper.
A 1994 US cent is zinc not copper, spend it.
1963 COPPER penny is worth half a billion dollars.
About $3
It's worth 2 cents for the copper.
1 cent
two dollars
About 2 cents.
It's worth 2 cents for the copper.
It's worth about two cents for the copper.
A 1994 US cent is zinc not copper, spend it.
face value
On average, about 3 cents.
A penny.