We have some specific limits in the American system that try to prevent such a tyranny of the majority from taking place. Take for example:
1) The Filibuster - you'll notice how difficult it has been for Democrats in the Senate, even with 59 seats, to overcome Republican filibusters and take measures to a floor vote. Even with huge majorities it took 14 months and some procedural maneuvering to pass health care reform. It wasn't meant to be used this way, but it does give the minority party some power.
2) Individual protections and limitations on power in the Constitution - The Bill of Rights trumps all government actions by the majority that ends up being tyranny over minority viewpoints and identities. The limits on power in the Constitution are absolute, and prevent one branch, say the Congress with most of government in it, from taking more control.
3) Independent judiciary - Federal judges are appointed for life, and answer only to the law and higher courts, not to the popular will of the majority.
Limited global democracy, in the form of the United Nations, is possible, but it is also pretty dysfunctional, and on a larger governmental scale simply doesn't work with 6.5 billion people.