The Desert Eagle was designed as a high-powered pistol with military applications in mind, although the weapon has never been adopted by any formal military organization around the world.
Since its introduction, the Desert Eagle has been a common sight in movies and TV shows (with these appearances often grossly overstating its power) meaning the pistol has remained popular despite it's lack of official use.
In Predator, Dutch's team (with the exception of Dillon) all carry Desert Eagles as their sidearm, although they are never used on screen. At one point, Dutch reaches for his pistol to defend himself from the Jungle Hunter, but finds he lost the weapon falling over a waterfall a few minutes previously.
In Predator 2, Mike Harrigan uses a brushed chrome .357 chambered Desert Eagle fitted with a laser sight as his primary sidearm throughout the film. He eventually loses it when it slips out of his holster while he is climbing between buildings in pursuit of the City Hunter.
In Alien vs. Predator, Max Stafford's mercenaries all carry nickel-plated Desert Eagles chambered in .44 Magnum as their sidearms, many of them fitted with green laser sights. The pistols are also briefly used by Rusten Quinn, Graeme Miller and Lex Woods.