Pennies from 1944 are Lincoln pennies. If the penny has the Lincoln Memorial on one side, it is worth its face value. If it is a wheat penny, it can be worth anywhere from 2 cents up to $500 depending on the mint.
Mint specification is important so as to know where it was crafted. Non minted ones are from Philadelphia which are worth up to 2- 60$..Uncirculated ones have much higher worth reaching up to 125-180$.