There are five types of gins. The four universally acknowledged types are London dry gin, Plymouth gin, Genever or Dutch gin, and Old Tom gin. Some people do not consider the fifth type, new American or international style gin, to be gin.
London dry gin is infused with different aromatic flavors during the 2nd and 3rd distillation process to give each brand a different flavor. It is typically a dry gin with a heavy juniper-infused taste that is used for classic martinis. Most London dry gins are not actually made in London. Some common brands are Tanqueray, Bombay Sapphire and Beefeater.
Plymouth gin is produced in Plymouth, England, and is a less dry gin that can be used in place of London dry gin. It has an earthier flavor and is infused with more roots than London dry gin.
Genever or Dutch gin is made with malt grains instead of the cereal grains that are typically used to make other types of gins. The malt grains give it a darker color and a flavor similar to some whiskeys. The most common brand of Genever or Dutch gin is Bols Genever.
Old Tom gin is a common gin used in the drink Tom Collins and is a sweeter gin. Hayman is a brand of Old Tom gin and is not as easy to find as other types of gin.
The new American style or international style refers to all other types of gin that are not infused with juniper berries but use the same type of distilling process. A well-known brand is Hendricks.