The immediate effects that the Declaration of the Independence had on the world was that it allowed for the connection, recognition, cooperation of foreign nations with the United States. The later effects was the colonization of several islands by the United States in the Spanish-American War. This was done in order to "spread democracy and upheld the similar American liberty" in other countries. Likewise, using the document as an example, other nations, such as Vietnam, fought for their independence from the their rulers.
However, one of its most profound effects would be its influence on the creation of the League of Nations, as well as the United Nations. Woodrow Wilson instigated the idea of a League of Nations based on the foundation in which the country was built on: the principles of democracy. It was for democracy that the United States fought the cold war for. Essentially, they were fighting for what they had declared for all of mankind nearly 200 years ago.