Alexander the Great and a number of imitators (such as Mehmed II, who was actually an impressive conqueror), and while I don't know if any others have made it an expressed desire, many have been conquered massive areas of land such as Genghis Khan, the Roman Empire, and the British Empire at it's height was so vast that it was said that the sun never set on it.
Today, in many ways, you could say that America has conquered the world, as American social, economic, and political hegemony is vast, powerful, and has permeated all but a few areas of human society as a whole.