America would remain a part of the British Empire
The American colonies would continue to be governed by the British Parliament, and the colonists would not have gained their independence. As a result, the United States would not exist today, and the political and economic history of North America would be very different.
No US constitution
Without a revolution, there would be no need for a constitution. The colonies would likely continue to be governed under the British system, with the king and Parliament holding all power. There would be no separation of powers, no checks and balances, and no guarantees of individual rights.
Fewer democratic revolutions
The American Revolution inspired many other democratic revolutions, such as the French Revolution and the Latin American Revolutions. Without the success of the American Revolution, these other revolutions might never have happened, or they might have been less successful.
European colonialism
The American revolution weakened European colonialism and helped inspire the rise of nationalism in Europe. Without the revolution, European colonialism might have continued for much longer, and the world might look very different today.