American English is, without doubt, the most influential and powerful variety of English in the world today. There are many reasons for this. First, the United States is, at present, the most powerful nation on earth and such power always brings with it influence. Indeed, the distinction between a dialect and a language has frequently been made by reference to power. As has been said, a language is a dialect with an army. Second, America's political influence is extended through American popular culture, in particular through the international reach of American films (movies, of course) and music. As Kahuna has pointed out, the internationally dominant position of a culture results in a forceful expansion of its language... the expansion of language contributes... to the prestige of the culture behind it. Third, the international prominence of American English is closely associated with the extraordinarily quick development of communications technology. Microsoft is owned by an American, Bill Gates. This means a computer's default setting for language is American English, although of course this can be changed to suit one's own circumstances. In short, the increased influence of American English is caused by political power and the resultant diffusion of American culture and media, technological advance, and the rapid development of communications technology.
While American English is a dialect with an army because the United States is the most powerful nation on the earth and such power brings with it influence, America's political influence is extended through American popular culture resulting in an expansion of its language, and the international prominence of American English is associated with the quick development of communications technology, which suggests American English is the most influential and powerful variety of English.