I ask this because of the Marcus Crassus line: "You can't really call yourself rich, unless you can aford your own army". So it got me wondering. When i mean army, i mean like something that could viably conquer and not just for protection.
One of the last private armies was under the private command of Leopold II of Belgium, who ruled the Congo as his personal colony - not administered through the Belgian government at all - from 1885 to 1908. His private army - totally distinct from the Belgian army - forced the natives to work through terror. These horrendous atrocities led to Belgium taking the colony from Leopold in 1908.
There're still multiple private military contractors who could probably conquer territory on their own if they chose to; however, international opinion - among other things - restricts them to contracting with nation-states rather than fighting on their own.
You should probably mention a country/region, because private people still own armies in certain parts of the world.