According to the United States Mint, a single modern penny weighs 2.5 grams. This means that 100 million pennies would weigh 250 million grams; or 551,155 pounds, 11.2 ounces.
However, this answer has a caveat. Contrary to popular belief, a modern penny is largely made from zinc and only plated with copper. According to About.com, prior to 1982, pennies were made from 95 percent copper, but those minted after 1983 are 97.5 percent zinc and only include a thin coating of copper. Since copper is heavier than zinc, the pennies made before 1983 weighed 3.11 grams. So, in essence, this answer could have several different values depending on how many pennies out of the 100 million were made before 1983.