According to the Oxford English Dictionary, a fallacy is "a mistaken belief, especially one based on unsound arguments." Or, more specifically in the case of logic, a fallacy is "a failure in reasoning which renders an argument invalid."

There are two primary categories of fallacies: formal and informal fallacies. Formal fallacies are errors in the structure of the argument itself, and are all some form of a [[https://en.wikipedia.org/wiki/Non_sequitur_%28logic%29|non sequitur]]. A list of formal fallacies can be found on Wikipedia [[https://en.wikipedia.org/wiki/List_of_fallacies#Formal_fallacies|here]].

An informal fallacy is a fallacy that is content-based. Consider the argument:

 * P1. If P, therefore Q.
 * P2. P.
 * C3. Therefore, Q.

There is no formal fallacy here, because the structure of the argument is sound. An informal fallacy, then, would be one where the content of the premises - that is, whatever P or Q is - means that the argument is wrong. For instance, take Bastiat illustrating the logical failures of socialist production: P is "The State provides Grain," and Q is "Only the State can provide Grain." Obviously, Q does not follow from P, even though the structure itself is proper.

There are many good resources that describe informal logical fallacies and give examples:

 * [[http://www.nizkor.org/features/fallacies|The Nizkor Project]]
 * [[http://www.logicalfallacies.info/|Logical Fallacies]]
 * [[https://en.wikipedia.org/wiki/List_of_fallacies#Informal_fallacies|Informal Fallacies (from Wikipedia)]]
 * [[http://www.cracked.com/article_19468_5-logical-fallacies-that-make-you-wrong-more-than-you-think.html|5 Logical Fallacies that Make You More Wrong than You Think]]

It's important to note that an informal fallacy doesn't necessarily mean that the conclusion itself is wrong; it just means that the reasoning used to get there was incorrect (see: "The Fallacy Fallacy").

A great chart:

{{http://1.bp.blogspot.com/-o9VE5tseuFk/T5FSHiJnu7I/AAAAAAAABIY/Ws7iCn-wJNU/s1600/Logical+Fallacy.JPG}}

Related: StatistFallacies (logical fallacies specific to statists)