The Cholla (Jumping Cactus) is very common in the desert in the Southwest and we often come across it when 4 Wheeling. Frequently it gets stuck in tires, shoes or legs when walking.
The first reaction is to use your hands to pull the cactus off. Big Mistake! When you do that you get painful spines in your hands. Even gloves don’t usually help.
Recently Gerry V. visited the Desert Museum near Tucson and they suggested using a comb, preferably a metal one, to slide under the cactus and “flick” it off. This leaves a few spines but most come out. If they are in bare skin the San Diego County Parks Department suggests spreading white (Elmers) glue on the affected area and let it dry. Once the glue dries you can then peel it off and the remaining spines should come out.