Rodeo is supposed to come from a Spanish word "rodear" which means "to encircle" and of course the Rodeo grew out of normal cattle ranch activities. Even before there were Rodeos for spectators, cowboys got together to test each other in contests related to their ranch and cattle work. Probably the first Rodeo (which wasn't called that as yet) was supposed to be held in Pecos Texas probably to celebrate the 4th of July. The first exhibition to offer "prize money" was held in Prescott, in the Arizona Territory on the 4th of July, 1888.
The cowboy riding and roping events of Buffalo Bill Cody's Wild West Show and other traveling shows became so popular that many western towns created annual Cowboy Tournaments (Round-ups and Frontier Days, etc) such as the Calgary Stampede started in 1912, and as Cheyenne Wyoming has done since 1897. The actual term "Rodeo" was first given to cowboy exhibitions in 1916 and the first indoor Rodeo was held at the Stockyards Coliseum in 1917 at Fort Worth, Texas.
Early Rodeos had Chuckwagon races, and Markmanship contests much like the format of Buffalo Bill's Wild West Shows, but in 1929 the Rodeo Association of America was formed in Salinas, California, and most of the events became standard as we know them today.
Some of the great names in Rodeo are Enos "Yakima" Canutt, (later to become a Hollywood stunt man) Will Rogers of Oklahoma, bronco rider Casey Tibbs of South Dakota (who was the model for the statue outside of the Rodeo Hall of Fame) and bull rider Jim Shoulders of Henryetta, Oklahoma.