This fallacy occurs when an arguer limits the conclusion to only one of two, often extreme, possibilities (either black or white) and refuses to acknowledge that some elements of both or a moderate conclusion (grey) could, in fact, be a possibility.  On an opposite note, there is also a fallacy called the "Middle-Ground" Fallacy where, in the interest of compromise, an arguer fallaciously tries to find the middle ground when a more extreme answer is, in fact, correct.  The Black-and-White Fallacy is often used when an arguer is trying to draw a line in the sand or to over-simplify a complex argument.  The following are examples of the "Black-and-White" fallacy:

Example: You either like bacon or you're wrong.

True.

Example: "America, love it or leave it!"

Or just don't have a strong love or dislike and stick around if you want and try to change the things you don't like...

Example: From Lyndon B. Johnson political ad: "We must either love each other, or we must die."

Couldn't we simply tolerate each other and not try to kill one another?

Example: George W. Bush after September 11 attacks: "You're either with us or against us."

Couldn't someone just opt out of taking a stance?

Example: "Only a Sith deals in absolutes."

Those darn black-and-white-fallacy-using Siths!

FALSE DILEMMA

The False Dilemma fallacy--a subcategory of the black and white fallacy--occurs when two options are pitted against each other when, in fact, they may not be mutually exclusive.  In these situations, it is possible that both options could be incorrect, both could be correct, or some combination of the two could reasonably be concluded.

Example: This meme.

The above meme starts off with an attempt at guilt by association (or a hint at covering one's self with the cross) and ends with an implied false dilemma.  Are helping refugees and helping homeless veterans mutually exclusive?  Couldn't the United States make initiatives to help both groups in need?