American whiskeys may often be categorized as pertaining to toastiness, spice and vanilla sweetness. This is in large part 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 stunning sweet flavors such as vanillin, and other flavor compounds.
Rye whiskey is made with a mash bill that mainly features rye. The result of this is a more spicy whisky with lots of complexity. Great examples include Sazerac rye whiskey and Pappy Van Winkle's Rye.
Tennessee whiskeys are essentially bourbons which undergo the "Lincoln County Process", developed by the world famous Jack Daniel. This involves filtering the spirit through sugar maple charcoal.
Moonshine is becoming increasingly popular, and you'll find a range here, as well as rarer artisanal US whiskeys such as single barrel and small batch bourbon, straight wheat and straight corn whiskey.