"Root beer was a traditional beverage and herbal medicine...used for treating cough and mouth sores. Commercial root beer was developed by Charles Elmer Hires in 1866...as root tea powder. In 1893 he began selling bottled, carbonated root beer. There was an upsurge in the popularity of root beer in the United States during the period of prohibition...Until Coke and Pepsi became popular.
Partial list of brands
Abita - Louisiana regional brand, made with local cane sugar
A&W Root Beer — Cadbury-Schweppes
Barq's — Coca-Cola
Barrelhead — Cadbury-Schweppes
Bickfords Sassparella (Australia)
Boylan Bottling Company
Bundaberg Root Beer — Australian brand of brewed drinks
Dad's Root Beer — Hedinger Brands, LLC
Dog n Suds
Frostie Root Beer
Hank's Root Beer
Hires Root Beer
IBC Root Beer — Cadbury-Schweppes
Jones Soda Root Beer
Mug Root Beer — PepsiCo
Point Premium Root Beer
Natural Brew Hand Crafted Draft Root Beer contains sweet birch, licorice root, sarsaparilla, cinnamon, clove, anise, wintergreen, and vanilla
Old Dominion Root Beer
Saint Arnold Brewing Company - Texas regional brand, made with cane sugar 
Sarsi — Coca-Cola Bottlers Philippines Inc.
Sioux City Sarsaparilla
Sprecher Root Beer
Stewart's Fountain Classics — Cadbury-Schweppes (Winner, 2006 World Cup of Root Beer)
Tommyknockers - When under the right lowlight, this brand glows in the dark.
Virgil's Root Beer — Reed's, Inc. "
(Taken almost verbatim from Wikipedia)