As the world becomes a more uncertain place and war still exists even in the 21st century, there are still countries in the world where you can find a complete state of peace. News of military conflict mars media outlets on a daily basis, so it's hard to believe that, actually, there are countries that have abolished their military.
Arguably the most famous of these is Iceland, which has now been recognized as the world's most peaceful country twice. The country has no offensive capacity and, instead, relies on civil homeland security services such as the coast guard, which patrols Iceland's surrounding waters and airspace.
However, Iceland is a member of NATO which provides total defense of member nations, so there is still military protection which NATO countries provide. Prior to 2006, the US maintained a military base on the island.
Other countries that have abolished the military include Costa Rica, Kiribati, Liechtenstein, Panama, Haiti, and the Vatican. Many are smaller countries who have no need for the military.