Cognac and Other Brandies
Brandy is made by creating a mash of grapes and some other fruit and allowing it to ferment into a wine. This 'wine' is distilled and then aged.
In France Cognac sets the standard, but there is also Armagnac and Calvados. Cognac is French Brandy from Cognac, a district in a place called Charente. There are six sub-regions in this area - Petite Champagne, Grande Champagne, Bois Ordinaires, Borderies, Fins Bois and Bois Bois. The Grande and Petite Champagne regions are supposedly the best producers of Cognac.
There are laws about how Cognac must be made. White grapes only of the Ugni Blanc, Colombard and Folle Blanche varieties. Cognac must be 90% one or more of these grapes. The remaining 10% can be any other white grape.
Cognac is aged in casks made from a type of oak called Limousin Oak. For some reason, Cognac aged less than 2 years cannot be exported the the United States. Cognacs and other Brandies are rarely labeled with the vintage because of blending processes that utilize spirits from different years to create consistent flavor. Most Cognac is dry with fruity and spicy notes.
Brandy
Cognac & Armagnac
In the Jerez district of Spain, the Palomino grape is used to create brandy. You will find it is a sweeter brandy and will typically have notes of caramel. Brandy from Jerez is aged in a solera just like Sherry (also made from Palomino grapes). In the solera there is periodical mixing of older brandies with new brandies (also a technique in making Sherry).
Brandy from the United States used to be considered subpar and not worth drinking. Today the brandy is of better quality and taste. Cognac-style methods are used in creation of brandy in America. One major difference is that the U.S. does not have the strict laws that France has in place for Cognac. In the United States, grapes such as Pinot Noir, Chenin Blanc, Chardonnay and Muscat are used to make extremely bold and complex brandies.
Beware the 'water of life'. Eau-de-Vie is the French name for clear spirits that are sweet, fruit-based brandies made from the leftovers of winemaking. Some of these are liquers. Pay attention or you might take home something you didn't want from your liquor store.

Armagnac is produced in an area of France called Gascony. Black Oak casks are used for aging and much of the process is the same as for Cognac. You will see vintages, unlike with Cognac.
Calvados is an apple brandy from Normandy, France. Sometimes pears are added. These are dry, spicy brandies.