American candy bars have been in some form of wrapper at least since Milton Hershey introduced chocolate to the American public in 1890. Just like candy bars themselves, modern chocolate bar wrappers also come in quite a variety.
Plastic "Foil" Wrappers
One of the most common types of chocolate bar wrappers consists solely of a thin layer of plastic, which tears easily. These types of wrappers, used on Snickers bars in the U.S. today, are the modern descendant of metal foil wrappers. Charleston Chew is another example of this type of wrapping
Two-layer Wrappers
Some candy bars have two wrappers: a metal foil wrapper that is in direct contact with the chocolate, and a paper wrapper surrounding the metal wrapper that shows the brand name of the product. Certain Hershey and Cadbury chocolate bars are wrapped in this fashion.
Folded Cardboard Wrappers
Some candy bars are encased in a folded piece of cardboard. One such chocolate bar is Toblerone (although, this does have an additional foil wrapper inside of the folded cardboard).
Metallised Foil Wrappers
Other types of candy bars are encased in a metallic foil wrapper, which peels open easily but makes much more of a "crinkly" sound when opened as compared to candies in a plastic wrapping. Candy bars featuring this type of wrapper include Twix, "Ice Cubes", and York Peppermint Patties.
Transparent Wrapper with Paper Labels
When manufacturers want to showcase a chocolate bar with an unusual texture, colour, or embossed design, they may package it in a clear wrapper with a paper label, in order to allow the consumer to better examine the product.