I'll mainly use Xenopedia as a source, which for the most part cites primary sources. This blog entry is also a good collection of information we have about the political situation.
Politically, the nations of Earth seem to have merged or united into different "empires". The one called the Three World Empire consists of Japan and the UK (which the merger of the British Weyland Industries/Corporation and the Japanese Yutani Corporation is either the result of, or played a large part in), as well as several developing countries. This empire seems to also be part of, or allied with, the United Americas somehow, although this has not been fleshed out.
North America, Central America and South America have merged (obstensibly as a response to the Three World Empire) and created a political entity called the United Americas. It doesn't seem to be a country, but a union of sovereign states (more akin to today's European Union), where the most powerful one seems to be the United States because of their position as a starfaring, colonizing power, and they also control the United States Colonial Marine Corps (USCM).
Private companies also have significant political pull, and are implied to control governments. AmArc is the name of one such company, which we don't know much about. "The Company", Weyland-Yutani, is obviously also very powerful on Earth. As they own several colonies, they often use the USCM for campaigns concerning their real estate in outer space, which probably explains how they want to use the Aliens as biological weapons, especially combined with the Washington Treaty which seemingly allows the United Americas to carry out incursions on colony worlds to assert their power (as was done at the colony Cristóbal to quell a strike and remove a leader).
Apparently, in 2600 AD (which is several centuries after the movies take place) Weyland-Yutani even bought the USCM (Alien: Invasion).