From Dragon Ball Encyclopedia, the ''Dragon Ball'' wiki
Factions and equipment
The Earthling Army is seen using forces very similar to that of the real world's military. Infantry men are, of course, the main group and use such equipment as different types of guns, grenades and other explosives, bazookas, and much more. In terms of vehicles, tanks, Jeeps, and Armored Cars seem to be used. The military is also composed of some sort of navy as large battleships, aircraft carriers, and high-powered jets are also employed. The King's Guard is a faction within the military, most notably seen during the King Piccolo Saga and later during the Cell Games Saga. There are also different types of Town Militia, which may be factions within the main military force as well.
It is unknown exactly why such a force exists as Planet Earth at the time of the main series is fully governed by one king, therefore it is unlikely that the same unified nation would go to war with itself. It is possible that this military force, however, has existed long before Earth's government had become unified. Another theory is that it was developed during Piccolo Daimao's reign of destruction, and has been kept ever since in case of another emergency such as that. It is plausible that this military is mainly used to maintain peace by combating such organizations as the Red Ribbon Army.
Dragon Ball Z
When two Saiyans – Vegeta and Nappa – threatened Planet Earth, the Earthling Army did prepare to attack only to be completely decimated by Nappa during his rampage. When Imperfect Cell killed and absorbed all of the civilians in Ginger Town, the Earthling Army arrived with an armada of tanks only for them to be destroyed by powerful energy beams from the monster's eyes. Later, when Cell threatened to destroy Planet Earth if not defeated in his tournament, King Furry sent his King's Guard in an attempt to destroy him again, this time believing he had brought more than enough infantry and vehicles, only to be defeated with ease once again.
Seven years later, with the threat of Majin Boo looming over the world, the Earthling Army was once again drawn into action. Despite an overwhelming force of battleships and jets, they were no match for the power of Majin Boo and were effortlessly destroyed yet again.