1944 Lincoln Cent Value is anywhere from a couple of cents up to $40, but to be worth $40 it must be graded and certified as MS67 (Mint State) by either PCGS or NGC grading companies.
A 1944 Lincoln cent was minted with either no mint mark (Philadelphia Mint), a D (Denver Mint) or an S (San Francisco Mint), and there is a rare variety called D over S mint mark. (The mint mark is just below the date, see images below.)
A 1944-D/S Lincoln cent is worth $30 and up to a few hundred dollars but in the higher grades they must be graded by either PCGS or NGC or ANACS grading companies.
Another rare 1944 Lincoln Cent is the examples struck on a steel planchet. These will stick to a magnet and are not copper. Only seven are known with a D mint mark and 2 are known with an S mint mark and thirty plus are known without a mint mark.
These can be worth $75,000 and up depending on the mint mark and the grade.
Not all Lincoln Cent Pennies are rare or worth much more than face value, as a matter of fact, most are common and worn. You will find rolls of them and they will look brown and often dark from circulation.