American whiskey is categorised as having a mostly toasty flavour with some added spice and vanilla sweetness. This is due to the generous use of new charred oak (predominant in most styles of US whiskey), and used exclusively in the production of Bourbon, which lends stunningly sweet flavour from vanillins, and other flavour compounds.
Rye whiskey is made with a mashbill that mainly features rye. The result of this is a more spicy whiskey with lots of complexity. Great examples include Sazerac rye whiskey, Rittenhouse Straight Rye and Pappy Van Winkle's Rye.
Tennessee whiskeys are essentially bourbons which undergo the "Lincoln County Process", developed by the world famous Jack Daniel's. This involves filtering the spirit through sugar maple charcoal.
White dog and Moonshine have becoming increasingly popular, and you'll find a range here, as well as rarer artisanal US whiskeys such as single barrel whiskey, grain whiskey, small batch bourbon, straight wheat and straight corn whiskey.