The modern Lincoln pennies minted since 1983 weigh 2.5 grams or 0.088 ounces. They consist of 97.5% zinc and 2.5% copper.
The older Lincoln pennies minted before 1982 weigh 3.11 grams and consist of 95% copper. These older Lincoln pennies include both the Lincoln Memorial series and the "Wheat" series. 1982 was the year that the weight and composition changed so both versions were minted during that year. To tell the difference, you can simply weigh the coins with a gram scale.
Before the Lincoln pennies were the Indian Head pennies. These pennies went through a few changes during the years. The first series of Indian Head pennies were minted in 1859. These pennies weigh 4.67 grams and are composed of 88% copper and 12% nickel. In 1864 the US government increased the weight to 3.11 grams and changed the composition to 95% copper and 5% tin and zinc.
There were one-cent coins that were minted before the Indian Head Penny. There is the Flying Eagle cent, the Braided Hair cent, the Matron Head cent, among others. However these coins are just considered to be one-cent pieces as they were never called pennies.
In addition, the United States minted a few different experimental cents that have different weights and compositions. The most well known experimental cent is the 1943 steel penny. It's a unique coin that weighs 2.7 grams. Another notable experimental cent is the 1974 aluminum cent that weighs just 0.937 grams.