The Circular Argument or "Begging the Question" fallacy, as it is sometimes known, is probably one of the most common fallacies employed in argument.  This fallacy seeks to win an argument based on a premise that is based on the actual question at hand.

Post Hoc Ergo Propter Hoc is the latin phrase for "after this, therefore because of this".  Unlike the other fallacies already presented, this fallacy is not an "internal error", but rather it is concerned with causality.  This fallacy has this structure: "A occurred before B.  Therefore A caused B to happen."  This fallacy is the foundation of most supersitions.

When we consider the validity of a conclusion, we should never reason in a vacuum.  In fact, many times during the course of debate, we may lose a debate simply because we have not thought outside of the box that our opponent has drawn for us.  Therefore, it is paramount to always think of other possibilties to match the facts of a particular question without conceding an opponent's conclusion.  The fallacy of false alternative occurs when we do not consider all of the relevant possibilities.

The Argumentum Ad Ignorantiam fallacy is a common one.  It relies on the lack of evidence for the opposing proposition in order to substantiate itself.  The most common application in our modern culture is our legal system.  A person is innocent until proven guilty.  If the prosecution fails to make the case against the defendant, his failure does not mean that the defendant is innocent - only that the burden of proof has not been met.  It does not mean that the defendant did not commit the crime.  As a general rule, it is the positive assertion that begins a discussion, and therefore the positive assertion that carries the burden of proof.  What is gratuitously asserted may be gratuitously denied.