The vast majority of the worlds nations have which system of government ?

As of today, the vast majority of world's government is under democracy, and the democratic government tree. This can include, but not limited too, federal,  representative, direct, etc.

For example, the US government employs both direct & indirect democracy (federal). In certain cases, the US people vote directly for any changes. But in general (such as the general election), the US votes indirectly, telling their representatives who to vote for.

Another example can be the United Kingdom, which also employs indirect democracy. They vote for members in the parliament, who then votes for the laws.

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