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.

I'd have to point to examples of the concentration of power that currently exists in the US as a good counter to the argument that democracy creates a tyranny of the majority.  Obviously not everyone would agree, but there are certainly a great number of people who feel that their opinions and even their votes are without consequence when it comes to the decisions made by their "representatives."

If you look at democracy in the American mold, I am not sure that a world-wide democracy is possible or even a great idea, but with more of a parlimentary system, that would allow for a greater number of viewpoints, it might be more of a possiblity.  But the current division of power in the sense that there are just two viewpoints is not one that would actually lend itself to an effective world-wide government.

Democracy does necessarily lead to tyranny of the majority if the majority truly wishes to tyrannize an unpopular minority of some sort.  I would argue that successes in minority rights (like the Civil Rights Movement) come only when the majority no longer hates the minority enough to want to oppress them.  Contrast that to the continuing inability of gay people to marry, which shows that they can be tyrannized (whether you think it is right or wrong to do so) by the majority.

Please note that the minority does not need to be sexual or racial or ethnic.  It can just as well be a political minority like radical environmentalists or a religious minority like polygamists.

As far as global democracy, if you mean one democratic government for the whole world, I'd say not in my lifetime or my kids' lifetimes, if ever.  Democratic societies have to be at least to some extent homogeneous and the world is really not homogeneous enough to allow people to respect and tolerate each other enough to sustain a democracy.