In most western countries, it is legal for law abiding citizens to own and wear bullet proof vest and other protective garments. Russia and other former Soviet republics allow responsible civilians to protect themselves by owning and wearing body armor, but these garments need to be registered and licensed their.
Why would you want to own and wear body armor?
There are quite a few reasons someone might need the security that comes from owning a well made, comfortable bullet resistant garment. Soldiers and private security personnel are often more comfortable using high quality, flexible body armor then the rigid vests used in military operations. Avid hunters like the added security a bullet resistant vest gives them in the field and 
blind, where trey may not be easily visible to other hunters. The world has become more dangerous, making workers in Jewelry stores, Pawn shops, and even 24 hour convenience stores, as well as the general public prime customers for protective garments.
Laws, regulations, and restrictions on ownership of Kevlar Vest vary widely from country to country. What is common to most countries is that citizens CAN own and wear protection garments, as long as they have not been convicted of, or committing certain crimes.
In most USA locations, there are no limitations on purchasing body armor. In Australia and Russia privately owned body armor must be licensed and registered. Canada, like the USA to the states, devolves the power to limit ownership of protective garments to its provinces. In the European Union, soft flexible body armor can be purchased by most every citizen, while Hard (ceramic) armor is designated a Military armament and its availability is limited to military applications. Like most everything else in the EU, additional restrictions can be imposed by member states and localities.
The summation is that basically, your are within your rights as a law abiding citizen, to purchase and use body armor; it is still wise to check what limitations you situation may put on that right.
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