They aren't. About a billion were minted.
You may be thinking of the famous 1943 pennies that were accidentally struck on bronze blanks instead of steel. Fewer than 20 of these are known to exist and the highest quality ones sell for tens of thousands of dollars.
1943 silver pennies
A rare date for wheat pennies would be 1909 S VDB.
No, the 1951 Lincoln cent is not rare.
Not really.
Many coins were minted for India in 1945. It is probably not rare.
They were minted at the Philidelphi(no mint-mark), Denver(D) mints. These pennies are not rare.
A rare date would be 1909-S VDB.
Uh, the word "everyday" means "ordinary or commonplace" so something that's commonplace can't be rare. If you're asking what are rare dates for Lincoln pennies please see the Related Question for more details.
NO, cleaning them will probably reduce their value
Please see Related Answers
US Coins issued before 1945 were comprised of 90% silver (penny excluded), and have a much higher values than those issued 1945 or after (in general). in 1942-1945, many pennies issued were made of steel (as copper was needed for the war). These war pennies also have a high value due to their rarity.
No. 2.4 BILLION were minted, and there are no known major varieties.