Appeal to Fear

Also called

Argumentum ad metum
Argumentum in terrorem
Scare'Em Straight

The slightly more subtle form of Appeal to Force, Appeal to Fear isn't a direct threat, but nevertheless is based on the idea that something terrible will happen unless you agree with a given position. The difference is that instead of

"Agree that 2 + 2 = 5, or else I'll beat you up."

you get

"Agree that 2 + 2 = 5, or else social order will collapse, criminals will go free, and they will beat everyone up."

This is a fallacy because whether an outcome is frightening has no relevance to whether the initial statement is true or not. Social order may collapse if you disagree that 2 + 2 = 5 (see Nineteen Eighty-Four), but that does not mean that 2 + 2 = 5. A type of Appeal to Consequences, where someone is supposed to be afraid of an outcome and therefore assume it to be true or false as a result. In marketing, this fallacy is known as FUD ("Fear, Uncertainty, and Doubt") and is applied to the use of vague criticisms of opposing products in order to try to persuade consumers to buy by brand.

Examples of Appeal to Fear include:

One of the most common variants is so-called "Hellfire" preaching, where the preacher focuses on the terrible things that will happen to people who don't accept his claims rather than anything positive about the religion in question (and, notably, without ever proving Hell exists in the first place, making this an appeal to consequences - leading to Pascal's Wager.)
Many old morality tales also use this fallacy by focusing on the horrible things that happen when children or adults break the rules; for example, The Boy Who Cried Wolf is traditionally eaten by a wolf for lying, as is Little Red Riding Hood for talking to a stranger.
This is also often used politically, playing off the fear of whatever is the scapegoat du jour (foreigners and ethnic minorities are common targets), and basically saying that if you vote for them, they'll pass legislation to "protect" the people from them.