Alcohol is the process that comes to mind when the word "fermentation" is mentioned, and rightfully so. The production of alcohol is one of the oldest controlled chemical interactions known in mankind's history. While beer is the most popular beverage produced, alcohol fermentation is found in many other drinks in many different cultures.
Beer:
The first evidence of beer brewing dates to around 5500 BCE, found at a
Sumerian village in the Zagros Mountains now known as
Godin Tepe. The Sumerians were the first to use a written language, and as a result, there are many documents from Sumer concerning brewing, beer, & its consumption. The beer drank in Sumer was made of malt, or malt bread, and played an important role in religion, daily life & diet, and medicine as well.
The Babylonians, whose empire conquered that of the Sumerians around 3700 BCE, had a beer made from barley or
emmer- a form of wheat, that was a staple of the Babylonian diet. They continued the Sumerian tradition of brewing, and were the ones responsible for spreading its knowledge and popularity south into Egypt, where it became one of the primary beverages for Egyptians from slaves to the Pharaoh.
How the art of brewing beer got from the Middle East to Europe is unknown, but there was evidence of brewing found in the village of Skara Brae in the Orkney Islands off of Scotland that date back to 3500-4000 in the Neolithic Period. Regardless of how brewing began in the west,
European monasteries played a large role in developing what we know as beer. Throughout Europe, many monastic societies allowed their monks a daily ration of beer, which began the tradition of monasteries brewing and selling beer for additional income.
Throughout history, there have been many methods used to flavor beer, and the first record of hops being used was written by a monk at a monetary in northern France around 822. However, it wasn't until the 1300s that hopped beer was introduced to England. Around that time, unhopped beer began going by the name "ale" with "beer" referring to its hopped counterpart. (Now, "ale," is used to refer to the fermentation temperature of the drink, along with "lager.")
(more can be read about the history of beer in Froth! by Mark Denny, and The Chemistry of Beer by Roger Barth)
Types of beer include:
Pilsner lager- from Pilsen, Bohemia (now Czech Republic), first marketed in 1852, and now the most common type of beer.
Chicha- from Central & South America, made from fermented maize
Opaque beer- from Africa, made with sorghum, is cloudy & still in the fermentation process when consumed
Cauim and masato- from Central & South America, made from cassava root (called manioc)
Sake- from Japan, made from a mold cultures grown on steamed rice.
Cider: The exact date of origins for brewing cider is unknown, but when England was invaded by the Greeks & Romans around 55 BC, fermented cider was already a part of the industry and culture amongst the locals. Cider is made from fermented fruit-usually apples, although in later years, other fruits were added to vary flavor
(more can be read about cider in this book, and in these government documents: 1, 2, 3, 4)
Mead: Made from a fermented honey mixture, the earliest archeological evidence can be traced
back to 6500-7000 BC in a village from Neolithic China. The drink has been mentioned in Hindu texts such as the Rigveda, which dates to around 1700-1100 BC, as well as texts by Aristotle (his Meteorologica) and Pliney the Elder. While most of Europe found grapes & wine making to be more economical, the art of brewing mead took hold in the northern areas, where the climate was much too harsh to properly cultivate vineyards, which is how mead has become to be associated so closely with Norse culture. There are countless versions and variants of the drink, a list of which can be found here.
Handbook of Animal-Based Fermented Food and Beverage Technology by 
