Countries that currently, or in recent history have depended upon the United States. Often used in an arrogant manner by some Americans who think that somehow showing support towards a nation should somehow give them a stake in that nation. Also often used by people noting that the culture of a country seems, or that a country shows a lot of support towards the US, or because of their cultural similarity to the US.
First usage: The United Kingdom due to the assistance from Americans in World War II, is sometimes a considered a 51st state.
Second usage: The United Kingdom is considered a 51st state due to their government's support of America in the Iraq war.
Countries that are largeley dependant on the United Stated for one reason or another such as trade, aid money or military support
Israel, Mexico, Canada
a non U.S. Country that is considered too supportive of the U.S. by it's residents
Canadian: "Canada is turning in the 51st state. I wish we were not so close to the U.S."