There are about 10 countries in the world that have minimal debt (rather than no debt). Minimal debt usually refers to countries where their debt to GDP ratio is under 20. These 10 countries, along with their Debt to GDP ratios, are:
Macao SAR - 0
Hong Kong SAR - 0.1
Brunei Darussalam - 2.5
Afghanistan - 6.8
Estonia - 8.5
Dem. Rep. of the Congo - 14.5
Solomon Islands - 14.6
Botswana - 14.9
Russian Federation - 18.7
United Arab Emirates - 19