A fallacy is a bad argument. Below are a number of what are called informal fallacies, common problems of reasoning that you will find in careless arguments.

Post hoc ergo propter hoc  fallacy ("after that, therefore because of that") -- a faulty or assumed cause-effect relationship that doesn't necessarily hold.  Example: The fact that the Bush administration has sold the rights to clean up the oil fields in Iraq to Halliburton proves that the war was about oil after all.

Hedging or equivocation -- changing the meaning of a word or concept from one part of an argument to the next. Example: We can never stop war, since even in families there are sometimes wars.

Red herring -- a decoy, an idea that is tossed into the argument to lead the line of reasoning in an irrelevant direction (from the practice of dragging a herring across a trail to throw off the scent in a hunt). Example: We haven't yet found any weapons of mass destruction in Iraq, but Syria is a potential problem, don't you think?

Ad hominem attack -- ("against the man") Attacking or criticizing the person rather than his ideas. Example: Our philosophy professor is against the war, but what can you expect? She's a Deadhead and wears a backpack to class.

"Either-or" fallacy (also called "false dilemma") -- Giving or acting as if there are only two choices when in fact there are more than two choices.  Example: In the current world situation, regarding terrorism, you are either with us or you're against us.

"Bandwagon"  fallacy (also called "appeal to common practice or common belief" ) -- accepting an idea because everyone else believes it or assumes it.  Example: We went after Saddam because of 9/11.

Appeal to false authority -- accepting an idea because someone you like accepts it, whether or not that person has the authority to know. Example: Martin Sheen is against the war and he plays the President on TV so I'm with him.

"Slippery slope" fallacy -- jumping to conclusions on the basis of one event or connection.  Example: If we had left Saddam in power, next every other despot in the region would get overconfident, then all the ones in Latin America and Africe, and before you know it we'd be threatened by the entire Third World.

"Straw man" or "Straw Dog" fallacy -- Putting words in someone's mouth to make them look bad or depicting them or their ideas in such a caricatured way as to trivialize them or their ideas. Example: Anti-war protestors walk around with their scruffy hair, slovenly dress, and sloppy thinking saying "Peace" like that was somehow a solution to  world political problems.