Collect the Whole Set!

Ad Hominem
Ad Hominem Tu Quoque
Appeal to Authority
Appeal to Belief
Appeal to Common Practice
Appeal to Consequences of a Belief
Appeal to Emotion
Appeal to Fear
Appeal to Flattery
Appeal to Novelty
Appeal to Pity
Appeal to Popularity
Appeal to Ridicule
Appeal to Spite
Appeal to Tradition
Bandwagon
Begging the Question
Biased Sample
Burden of Proof
Circumstantial Ad Hominem
Composition
Confusing Cause and Effect
Division
False Dilemma
Gambler's Fallacy
Genetic Fallacy
Guilt By Association
Hasty Generalization
Ignoring A Common Cause
Middle Ground
Misleading Vividness
Personal Attack
Poisoning the Well
Post Hoc
Questionable Cause
Red Herring
Relativist Fallacy
Slippery Slope
Special Pleading
Spotlight
Straw Man
Two Wrongs Make A Right

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In order to understand what a fallacy is, one must understand what an argument is. Very briefly, an argument consists of one or more premises and one conclusion. A premise is a statement (a sentence that is either true or false) that is offered in support of the claim being made, which is the conclusion (which is also a sentence that is either true or false).

There are two main types of arguments: deductive and inductive. A deductive argument is an argument such that the premises provide (or appear to provide) complete support for the conclusion. An inductive argument is an argument such that the premises provide (or appear to provide) some degree of support (but less than complete support) for the conclusion. If the premises actually provide the required degree of support for the conclusion, then the argument is a good one. A good deductive argument is known as a valid argument and is such that if all its premises are true, then its conclusion must be true. If all the argument is valid and actually has all true premises, then it is known as a sound argument. If it is invalid or has one or more false premises, it will be unsound. A good inductive argument is known as a strong (or "cogent") inductive argument. It is such that if the premises are true, the conclusion is likely to be true.

A fallacy is, very generally, an error in reasoning. This differs from a factual error, which is simply being wrong about the facts. To be more specific, a fallacy is an "argument" in which the premises given for the conclusion do not provide the needed degree of support. A deductive fallacy is a deductive argument that is invalid (it is such that it could have all true premises and still have a false conclusion). An inductive fallacy is less formal than a deductive fallacy. They are simply "arguments" which appear to be inductive arguments, but the premises do not provided enough support for the conclusion. In such cases, even if the premises were true, the conclusion would not be more likely to be true.

Examples of Fallacies

Inductive Argument
Premise 1: Most American cats are domestic house cats.
Premise 2: Bill is an American cat.
Conclusion: Bill is domestic house cat.


Factual Error
Columbus is the capital of the United States.


Deductive Fallacy
Premise 1: If Portland is the capital of Maine, then it is in Maine.
Premise 2: Portland is in Maine.
Conclusion: Portland is the capital of Maine.
(Portland is in Maine, but Augusta is the capital. Portland is the largest city in Maine, though.)


Inductive Fallacy
Premise 1: Having just arrived in Ohio, I saw a white squirrel.
Conclusion: All Ohio Squirrels are white.
(While there are many, many squirrels in Ohio, the white ones are very rare).

http://www.nizkor.org/features/fallacies/

(got me a #1)