The following explanation as to why we yell, "Geronimo!" when we jump out of planes is from "The Book of Totally Useless Information" by Don Voorhees: Well, we don't all jump out of planes or there would be a lot more yelling going on, and not necessarily "Geronimo!"
Believe it or not, this expression does go back to the time of Geronimo, the great Native American leader, who is first credited with its use. Legend has it that while being pursued by the U.S. Cavalry near Medicine Bluffs, Okla., the Apache chief was trapped at the edge of a cliff. Rather than surrender, he leaped off the cliff on horseback, yelling out his name, "Geronimo!" to taunt the troops. He survived this jump and rode away to a short-lived freedom.
During World War II, the paratroopers in the 82nd Airborne Division, at Fort Bragg, N.C., having heard of the legend, began shouting, "Geronimo!" as they jumped from their planes.
Geronimo's given name was Goyahkla, Native American for "one who yawns," but the Mexicans gave him the name Geronimo, after St. Jerome, whom they pleaded with for help after a particularly bloody battle with the seemingly invincible Native American.