American wild ale is a style of beer

Beer style

Beer style is a term used to differentiate and categorize beers by various factors such as colour, flavour, strength, ingredients, production method, recipe, history, or origin....

 pioneered by American microbreweries which is characterized by the use of yeasts other than Saccharomyces cerevisiae

Saccharomyces cerevisiae

Saccharomyces cerevisiae is a species of yeast. It is perhaps the most useful yeast, having been instrumental to baking and brewing since ancient times. It is believed that it was originally isolated from the skin of grapes...

for fermentation. Beers in this style are typically fermented using a strain of brettanomyces

Brettanomyces

Brettanomyces is a non-spore forming genus of yeast in the family Saccharomycetaceae, and is often colloquially referred to as "Brett". The genus name Dekkera is used interchangeably with Brettanomyces, as it describes the teleomorph or spore forming form of the yeast. The cellular morphology of...

for part or all of the fermentation.
The use of brettanomyces or other yeasts can result in a funky, complex flavor profile can be inappropriate to other beer styles.
Examples include Jolly Pumpkin Perseguidor, Avery 15, Ommegang

Brewery Ommegang

Brewery Ommegang is a Belgian brewery located near Cooperstown, New York that specializes in Belgian-style ales.-History:Ommegang began brewing Belgian-style ales in 1997...

 Ommegeddon, and Avery Brabant.

The style is recognized by the BeerAdvocate website, but not by the BJCP