It is always interesting how people from different areas of the world sound different even though they are speaking the same language. For example Americans sound very different to the English even through both speak English and the original settlers of America were English. The development of accents happens when groups are separated from each other by distance. Accents are also influenced by other cultures and languages that are part of the community. Many different cultures have contributed to the development of the American accent.
It is thought that the American accent is closer to the original British accent than what is spoken in England today. This is largely due to the fact that not many Cockneys migrated to America. It is difficult to pinpoint exactly when the accent became different, but as America became more independent and had less contact with the British Empire new ways of speaking would have evolved. The American accent has also been influenced by the migration of people from German, Scotland, Ireland and other European countries. The language was even influenced by the many African slaves that became part of American society.
Many Asian countries that speak English do so with an American accent mainly due to the influence of media and the movie industry. America itself has a number of different accents with the accents of Northern America being very different to that of southern America. General American or Standard American English is derived from the mid west American Accent and is what you hear most predominantly when watching American TV shows or movies.