Here is my list of presidential, parliamentary and other regimes as of 17 October 2016. A list of countries with semi-presidential constitutions is posted separately.
Afghanistan, Angola, Argentina
Benin, Bolivia, Brazil, Burundi
Chile, Colombia, Comoros, Rep. of Congo, Costa Rica, Côte d’Ivoire, Cyprus
Djibouti, Dominican Rep.
Ecuador, El Salvador, Equatorial Guinea
Ghana, Guatemala, Guinea, Guyana
Kazakhstan, Kenya, Rep. of Korea
Malawi, Maldives, Mexico
Palau, Panama, Paraguay, Philippines
Seychelles, Sierra Leone, Singapore, Sudan
Uganda, USA, Uruguay, Uzbekistan
Parliamentary (M = Monarchy, R = Republic)
Albania (R), Andorra (M), Antigua & Barbuda (M), Australia (M)
Bahamas (M), Bahrain (M), Bangladesh (R), Barbados (M), Belgium (M), Belize (M), Bhutan (M)
Cambodia (M), Canada (M)
Denmark (M), Dominica (R)
Estonia (R), Ethiopia (R)
Germany (R), Greece (R), Grenada (M)
India (R), Iraq (R), Israel (R), Italy (R)
Jamaica (M), Japan (M), Jordan (M)
Lao PDR (R), Latvia (R), Lebanon (R), Lesotho (M), Liechtenstein (M), Luxembourg (M)
Malaysia (M), Malta (R), Mauritius (R), Monaco (M), Morocco (M)
Nepal (R), Netherlands (M), New Zealand (M), Norway (M)
Pakistan (R), Papua New Guinea (M)
St Kitts & Nevis (M), St Lucia (M), St Vincent & the Grenadines (M), Samoa (M), Solomon Islands (M), Somalia (R), Spain (M), Swaziland (M), Sweden (M)
Thailand (M), Trinidad & Tobago (R), Tuvalu (M)
Presidentialism (i.e. popular presidential election) with no PM but cabinet accountability
Presidentialism (i.e. popular presidential election) but president accountability to legislature but not cabinet
Parliamentarism (i.e election of the president by the legislature) with no PM and no head of state/govt accountability and no cabinet accountability
Eritrea, Micronesia, Suriname, Switzerland
Parliamentarism (i.e election of the president by the legislature) with no PM but head of state/govt accountability and cabinet accountability
Botswana, Cuba, Kiribati, Marshall Islands, Nauru, South Africa
Parliamentarism (i.e election of the president by the legislature) with head of state, PM and cabinet accountability
Brunei, Monaco, Oman, Qatar, Saudi Arabia, Tonga, UAE
Bosnia & Herz., China, Iran, North Korea, Myanmar, San Marino
Libya, South Sudan
A broader statement of my philosophy about how regimes should be defined and the definitions themselves can be found at the link below.
The two basic definitional criteria are the method of selection of the head of state and whether or not the cabinet is responsible to the legislature. Obviously, other criteria could be used to refine the list of regimes further. So, for example, I use Shugart and Carey’s distinction between premier-presidential and president-parliamentary regimes to identify sub-types of semi-presidentialism. Here, though, I stick to the two criteria above, which is scientific standard.
The countries are classed on the basis of their current constitution. Bear in mind that the list does not take into account whether a country is democratic. For example, in Bahrain there is a form of collective cabinet responsibility. That is to say, there is a constitutional process by which the legislature could bring down the government. The politics of Bahrain, not least the monarch-appointed chamber that forms one house of the legislature, means that this is very unlikely ever to happen. However, constitutionally, Bahrain meets the requirements for parliamentarism, even if it is unequivocally autocratic. To put it another way, some presidential countries are, in practice, more presidential than others. Some parliamentary countries are, in practice, more prime ministerial than others, etc. The definitions used here are not designed to capture political practice. They are designed to capture constitutional rules.
I welcome corrections and comments.