I'm curious to know if the penny I have is worth money. It doesn't have a letter stamped under the date. Does this make the penny counterfeit?

Some don't have mint marks. A wheat penny from 1944, if a steel penny, is worth a lot. Copper maybe 10c-$3 depending on condition

Without proper appraisal its worth a penny. Condition is key to any appraisal.

I will agree, worth a lot? Normally you will not be rich, but it can be worth 200 or more times its face value.

1944 Lincoln Wheat Cent - Uncirculated - Wheat 1c

No mint, 1.79, unsold. The fees and shipping will cost this seller more than 1.00. Don't count on any value.
Good way to start getting into coins, I guess. I buy silver coins at times.

There are a number of good answers already but here goes...

Your one cent coin (referred to as a "penny" by most people) can have value as a collectible or for the value of the copper.

In regard to the value of the metal, it is illegal to smelt them in the US but legal everywhere else in the world - including in Canada and Mexico. US cents were made of 95 percent copper and the rest of tin and zinc up until 1982. The value of the copper varies according to demand for industrial metals, but generally will be about two cents or more. During 1982, composition of the cent was changed to almost all zinc, with a copper plating on the outside. So, if you weigh a 1981 or earlier cent in one hand and a 1983 or later (this is presuming both coins are not badly worn; wear reduces the weight) in the other hand, the 1983 will be perceptibly lighter. It will also sound different if you drop it on a table.

The steel cent referred to in an earlier response had a steel planchet with zinc plating and was an experiment during WW2 in 1943 to try to save the copper for use in war matériel, primarily for bullet and shell casings. The mint switched back to recovered shell casings in 1944, but the occasional unstruck steel planchet was caught up in the machinery after they shut down 1943 cent production. When one of these stuck planchets came loose when they started to produce 1944 cents, there would be a steel cent with the 1944 date, which is a rare and highly sought-after collectible.

A 1944 cent in "new" uncirculated condition also has value as a collectible. If this is the case, please do nothing to "clean" the coin, as chances are you will damage it.

Hope this boring explanation helps.