It depends by what you mean "valuable" all pennies dated 1958 and prior are worth more than face value, at a few cents more than face in all except for the very lowest grade (for some ultra-rare cents, even a poor condition cent can be worth hundreds of dollars). In general, the older the coin, the more valuable. But for wheat cents, the rare dates are:
1909-S VDB
1909-S no VDB
1914-D
1922 without a mintmark
1931-S
1943 COPPER penny (any 1943 cent that is magnetic is NOT rare)
1944 STEEL penny (any 1944 cent that is not magnetic is NOT rare)
On both the 1943 and 1944 pennies, beware of fakes! There are many, many, copper plated steel cents or altered dates (genuine 1948 cents with the 8 altered to look like a 3, etc.)
In an auction house.
Yes, there are valuable copper US pennies, typically those that are made of mostly copper and are older. Pre-1982 pennies are mostly copper (95% copper, 5% zinc), making them more valuable than post-1982 pennies which are mostly zinc. Some valuable copper pennies include the 1943 copper penny, 1909-S VDB, and 1955 doubled die penny.
Because people do collect them.
1937 penny
Wheat pennies from the 1940's and 50's are 5-10 cents.
Not really, as there are billions of them already in circulation.
Not any time soon. There are billions of them in circulation.
The sauce has acid in it, which cleans pennies. Keep in mind that a penny that might be rare and valuable has little value if it has been cleaned.
Generally, coins are valuable because of the price of the metals they are made from, but if you mean in a collectible way: One thing that makes a penny valuable is the date. They older the coin usually the more valuable. Another thing is the mintmark. For example 1943 pennies with a "S" mintmark are more valuable than pennies with no mintmark. Another thing is the condition of the coin. The less ware it has the more it's worth.
it depends wheather or not you are interested in them and think they are valuable.
Yes, less than 6 are known.
1909-S-vdb, 1914-D, 1931-S and others.