It certainly does exist as an aspiration of existing Western powers led by the United States. The conspiracy theories that you have seen bandied about since the advent of the internet are the paranoid reactions to the idea of a New World Order, or one world government.
Woodrow Wilson talked about a one world democracy after the holocaust of WWI. His “League of Nations” was just the beginning. He wished for a one-world Parliament where every country would have a voice and hopefully avoid a reprise of the wanton annihilation of 20 million people like that which occurred in the four years between 1914–1918.
Next up was Adolf Hitler. He proclaimed many times in his speeches that the Nazi Third Reich’s ultimate aim was to “hammer and forge” the countries of the world together with “blood and iron” (reminiscing Bismark) into one New World Order, which he made very clear was about “Liebensraum”, or “Living space” exclusively for the Aryan race and the enslavement and destruction of all other races including their “inferior” cultures.
So, when George H. W. Bush used that exact term, “New World Order”, 46 years later in a speech to the US Senate in 1991, many people were made quite uncomfortable. The speech described a world united under Capitalism and guided by the Free Market. What was missing was the word democracy and, as everybody knows, Capitalism can do very well for itself without the hindrance of human rights and the voice of the complaining masses.
Thus, the plethora of wild and not-so-wild conspiracy theories with which you and I are familiar.