I often use the phrase Hegemony on this blog, especially when describing the United States, though not exclusively. In this post, for example, I refer to Russia re-establishing regional hegemony. Russia as regional hegemon has gained more weight in recent years. We've seen Russian involvement in Ukrainian politics (the other side in the "Orange Revolution"). We've seen Russia be overt about the potential for military action in Poland. And most strikingly, we've seen Russia wage war against neighboring Georgia and in return establish military bases in South Ossetia and Abkhazia. These are all the actions of a regional hegemon - influence in bordering countries, a foreign policy that seeks to tie the fates of satellite states to a bigger patron, defiance of other nations when it comes to neighboring states, and a willingness to use military force to achieve these ends. Russia is no doubt a regional hegemon.
But the sense of hegemony I tend to use is that of the United States and it's hegemony over the world. The United States is, at present, the world's foremost military power, and the world's most influential military. The United States, a country located entirely in the Western Hemisphere, has priorities and specific territorial concerns on every continent. The United States has done this for over half a century.
There's more minute detail that one can put into defining a global hegemon, but I think this map will suffice. As pointed out on BoingBoing, the 1-100 category probably includes embassy guards (which are good, and represent sound diplomacy instead of overt military control), but that aside, the map is still a decent documentation of where the US military exercizes it's influence. And the short of that "where" is "everywhere".