Fallacies

• Tu quoque ("you too"). This is the fallacy of defending an error in one's reasoning by pointing out that one's opponent has made the same error. An error is still an error, regardless of how many people make it. For example, "They accuse us of making unjustified assertions. But they asserted a lot of things, too!" 
• Straw man. This is the fallacy of refuting a caricatured or extreme version of somebody's argument, rather than the actual argument they've made. Often this fallacy involves putting words into somebody's mouth by saying they've made arguments they haven't actually made, in which case the straw man argument is a veiled version of argumentum ad logicam. One example of a straw man argument would be to say, "Mr. Jones thinks that capitalism is good because everybody earns whatever wealth they have, but this is clearly false because many people just inherit their fortunes," when in fact Mr. Jones had not made the "earnings" argument and had instead argued, say, that capitalism gives most people an incentive to work and save. 
• Post hoc ergo propter hoc (after this, therefore because of this). This is the fallacy of assuming that A caused B simply because A happened prior to B. A favorite example: "Most rapists read pornography when they were teenagers; obviously, pornography causes violence toward women." 
• Red herring. This means exactly what you think it means: introducing irrelevant facts or arguments to distract from the question at hand. For example, "The opposition claims that welfare dependency leads to higher crime rates -- but how are poor people supposed to keep a roof over their heads without our help?"
• Slippery slope. A slippery slope argument is not always a fallacy.  A slippery slope fallacy is an argument that says adopting one policy or taking one action will lead to a series of other policies or actions also being taken, without showing a causal connection between the advocated policy and the consequent policies. A popular example of the slippery slope fallacy is, "If we legalize marijuana, the next thing you know we'll legalize heroin, LSD, and crack cocaine." 
• Cum hoc ergo propter hoc (with this, therefore because of this). This is the familiar fallacy of mistaking correlation for causation -- i.e., thinking that because two things occur simultaneously, one must be a cause of the other. A popular example of this fallacy is the argument that "President Clinton has great economic policies; just look at how well the economy is doing while he's in office!"
• Circulus in demonstrando (circular argument). Circular argumentation occurs when someone uses what they are trying to prove as part of the proof of that thing. Here is one of my favorite examples (in pared down form): "Marijuana is illegal in every state in the nation. And we all know that you shouldn't violate the law. Since smoking pot is illegal, you shouldn't smoke pot. And since you shouldn't smoke pot, it is the duty of the government to stop people from smoking it, which is why marijuana is illegal!" Circular arguments appear a lot in debate, but they are not always so easy to spot as the example above.
• Argumentum ad numerum (argument or appeal to numbers). This fallacy is the attempt to prove something by showing how many people think that it's true. But no matter how many people believe something, that doesn't necessarily make it true or right. Example: "At least 70% of all Americans support restrictions on access to abortions." Well, maybe 70% of Americans are wrong! 
• Argumentum ad nauseam (argument to the point of disgust; i.e., by repitition). This is the fallacy of trying to prove something by saying it again and again. But no matter how many times you repeat something, it will not become any more or less true than it was in the first place. 
• Argumentum ad ignorantiam (argument to ignorance). This is the fallacy of assuming something is true simply because it hasn't been proven false. For example, someone might argue that global warming is certainly occurring because nobody has demonstrated conclusively that it is not. But failing to prove the global warming theory false is not the same as proving it true. 
• Argumentum ad hominem (argument directed at the person). This is the error of attacking the character or motives of a person who has stated an idea, rather than the idea itself. The most obvious example of this fallacy is when one debater maligns the character of another debater (e.g, "The members of the opposition are a couple of fascists!"), but this is actually not that common. A more typical manifestation of argumentum ad hominem is attacking a source of information
• Argumentum ad antiquitatem (the argument to antiquity or tradition). This is the familiar argument that some policy, behavior, or practice is right or acceptable because "it's always been done that way." This is an extremely popular fallacy in debate rounds; for example, "Every great civilization in history has provided state subsidies for art and culture!" But that fact does not justify continuing the policy.  
• Argumentum ad populum (argument or appeal to the public). This is the fallacy of trying to prove something by showing that the public agrees with you. 
• Argumentum ad verecundiam (argument or appeal to authority). This fallacy occurs when someone tries to demonstrate the truth of a proposition by citing some person who agrees, even though that person may have no expertise in the given area.  
• Nature, appeal to. This is the fallacy of assuming that whatever is "natural" or consistent with "nature" (somehow defined) is good, or that whatever conflicts with nature is bad.
• Non Sequitur ("It does not follow"). This is the simple fallacy of stating, as a conclusion, something that does not strictly follow from the premises. For example, "Racism is wrong. Therefore, we need affirmative action."
• Petitio principii (begging the question). This is the fallacy of assuming, when trying to prove something, what it is that you are trying prove. For all practical purposes, this fallacy is indistinguishable from circular argumentation.