A logical fallacy is any sort of mistake in reasoning or inference, or, essentially, anything that causes an argument to go wrong. There are two main categories of fallacy, Fallacies of Ambiguity and Contextual Fallacies:
Fallacies of Ambiguity: a term is ambiguous if it has more than one meaning. There are two main types:
equivocation: where a single word can be used in two different senses.
amphiboly: where the ambiguity arises due to sentence structure (often due to dangling participles or the inexact use of negatives), rather than the meaning of individual words.
Contextual Fallacies: which depend on the context or circumstances in which sentences are used. There are many different types, among the more common of which are:
Fallacies of Significance: where it is unclear whether an assertion is significant or not.
Fallacies of Emphasis: the incorrect emphasis of words in a sentence.
Fallacies of Quoting Out of Context: the manipulation of the context of a quotation.
Fallacies of Argumentum ad Hominem: a statement cannot be shown to be false merely because the individual who makes it can be shown to be of defective character.
Fallacies of Arguing from Authority: truth or falsity cannot be proven merely because the person saying it is considered an "authority" on the subject.
Fallacies of Arguments which Appeal to Sentiments: reporting how people feel about something in order to persuade rather than prove.
Fallacies of Argument from Ignorance: a statement cannot be proved true just because there is no evidence to disprove it.
Fallacies of Begging the Question: a circular argument, where effectively the same statement is used both as a premise and as a conclusion.
Fallacies of Composition: the assumption that what is true of a part is also true of the whole.
Fallacies of Division: the converse assumption that what is true of a whole must be also true of all of its parts.
Fallacies of Irrelevant Conclusion: where the conclusion concerns something other than what the argument was initially trying to prove.
Fallacies of Non-Sequitur: an argumentative leap, where the conclusion does not necessarily follow from the premises.
Fallacies of Statistics: statistics can be manipulated and biased to "prove" many different hypotheses.
These are just some of the most commonly encountered types, the Internet Encyclopedia of Philosophy page on Fallacies lists 176!