The armored car, as a military vehicle, although it has been overshadowed by its larger cousin, the Main Battle Tank, probably is used in much greater numbers and in much greater frequency in many of the world's armed forces. An armored car can be defined as a wheeled (as opposed to tracked) vehicle that has armor thick enough to guard against at least shrapnel and small arms fire. Of course, as a military vehicle, the armored car almost always carries arms, usually of a light nature.
The armored car's military service actually dates back further than the tank, with the Royal Navy using them to patrol its air bases at the outbreak of World War I, making it a sort of army for the air forces of the navy. However, with the exception of some reconassiance missions, the armored car did not play much of a role on the Central Front during that war. It was used quite gainfully in the Middle Eastern front, however, being well suited for desert warfare.
The 1920s saw much usage of Armored Cars, not in military action, but in police action. The British found them very useful in Ireland, India and Palestine, and in their occuptation army in Germany. Other countries also begin building armored cars, usually for the purpose of reconaissance units.
In World War II, the usage of the armored car was parallel to their usage in World War I. Besides for some reconaissance missions and some desert fighting, armored cars were never used en masse in battles. World War II was perhaps the last war between large nation states, so since that point there has not been many chances to test the idea of armored cars as being an important part in conventional warfare.
At the front of this writeup, however, I said that armored cars played a larger role in warfare than tanks. I say this because conventional warfare between the regular armies of nation states makes up a very small percentage of what goes under the heading of warfare. As I alluded to above when discussing the interwar usage of the armored car by the British, one of the main usages of the military armored car is in police actions. Personally, I find such usage to be morally questionable at best, but from a purely objective military viewpoint, it makes perfect sense.
On any kind of conventional battlefield, an armored car would not survive long. Especially in the modern days with attack helicopters and depleted uranium rounds, an armored car doesn't have the neccesary armor to live for long. However, advanced armor piercing weapon aren't even neccesary to take out an armored car. Even a well trained
infantry squad armed with LAWS and a .50 calibre machine gun would have a fair chance of disabling most armored cars now in service.
However, how much the armored car is dwarfed on the battle field is also how much it would dwarf normal people in a riot control or counter-insurgency situation. On the battlefield, a machine gun is considered a rather light weapon. In a riot control situation, a fully automatic assault rifle is considered a heavy weapon, and modern armored cars are bulletproofed against them. On top of that, even in areas of the world with cohesive rebel militias with some training, the size and armament of an armored car are intimidating. For that reason, many countries, from Great Britain to Israel to Brazil to South Africa range a force of armored cars armored and armed to deal with irregular warfare operations ranging through the spectrum from riot control to counter-insurgency. The United States has traditionally forsaken the usage of armored cars, besides a small number of military police vehicles used to patrol United States Navy and United States Airforce bases. This is perhaps seen as a good sign that the Pentagon doesn't have many plans for engaging in warfare against the United States population.
So, moral objections aside, the basic reason the armored car is kept in service by so many armies around the world despite its low battle field survivability is its ability to conduct irregular warfare.