There are loads. But some common ones:

• Ad hominem To attack the person not the argument: "We should increase taxes", "Don't listen to him, he only showers once a week".

I've been getting a lot of replies about this one. An ad hominem only occurs if you ignore the argument and attack the person to undermine the argument. "It's hot outside, let's all go for ice-cream." "That's a bad idea. I'm diabetic, you moron" is not ad hominem. It's not a very nice response, but he still counters the argument with a reason. "Men are more likely to drink-drive, so all men should be banned from driving." "You're a massive idiot." still isn't really ad hominem; he is attacking the person, but it is more like an insult than a counter argument. "Board games are the root of all evil. If we ban them then crime will go down." "You are clearly uneducated and a fool, so this cannot be true." is an ad hominem fallacy. And now I've probably made everything more confusing.

• Circular Reasoning Where the reason relies on the conclusion being true. "God exists because the Bible says so; Bible is true since it's the word of God".

• Slippery slope The assumption that accepting one thing will lead to increasing undesirable other things. "If we let the immigrants in then they will take our jobs, leaving us homeless and then our children will be forced to work as prostitutes for food. Is that what you want? Child prostitutes?"

• False Dilemma Forcing or suggesting there are only two possible options in a situation, where really there are many. "Steve insulted my mother, so I had to either punch him or be forever known as a wuss"

• Tu quoque Literally you too (I think). Basically saying that if you don't do it, why should I? "My doctor told me to lose weight, but what does he know? He's fatter than me!"

• Appeal to Authority Where a statement by an irrelevant authoritative figure or group is used. "Dr Steve says the vaccine causes cancer, so that vaccine must be banned." "Tiger Woods says this 10 bladed razor is way better than a 3 bladed one. The 7 extra blades therefore clearly make a difference."

• Appeal to Popularity Where if a sizeable group of people belief in something, the belief must be correct. "300,000 Indians eat rice every day, therefore it must be healthy."

• Appeal to Ignorance Where you assume something is true because it hasn't been proven false. Your standard "I don't know, therefore aliens".

• Loaded Question Asking a question that presumes a certain fact. "What's your opinion on the immigrants that are ruining our society?" assumes immigrants are ruining our society, and by answering it directly you agree with this statement.

• Straw Man Misrepresent the argument to make it easier to knock down. "We should give free fruit to school kids", "Yeah, let's just give everyone free food. That would just lead to obesity and a greater deficit".

• Post Hoc (ergo propter hoc) Claiming that because something happens after something else, the first caused the second. "I wore my green socks today, and then found out my wife was leaving me. I didn't know she hated them that badly."

• Gamblers' Fallacy Believing that a deviation in a series of (independent) chance events will soon be met by a deviation the opposite way. "I've given birth to six boys. My next kid is definitely a girl!"

• Middle Ground Saying that a compromise between two extreme position is the correct one, solely because it is in the middle. "Schools are being forced to teach both creationism and the theory of evolution. The truth must be somewhere in between; they should teach the theory of creatioevolutionism."

• Appeal to Emotion Relying on manipulating emotions rather than a solid argument. "Look at this poor little dog. Look at it! He looks so miserable and depressed. We should take him home and look after him." or "Meth. Not even once."

• "Fallacy" Fallacy The fallacy you might use after reading this list. An argument contains a fallacy, therefore the conclusion is wrong. "The Meth. Not even once. campaign is just one massive appeal to emotion fallacy. Therefore there is no reason to stop doing meth."

I've probably forgotten a few.

Examples are meant to be exaggerated. In real life they are often more subtle, and the names aren't important as long as you recognise that there's something wrong.

Edit: Adding more fallacies that others have mentioned for a more complete list.

Edit: Added Middle Ground, fixed some grammar errors, formatting.

A logical fallacy is a failed attempt at using logic. Logic is kind of like math in that it has rules. If you said that 2+2=5, you would have made an error. A logical fallacy is similar to this in that you can attempt to put together some facts and use a faulty mechanism for reasoning to lead you to a conclusion that may or may not be the right one.

A very common one is the use of "ad hominem" attacks. An example would be if you and I were having a disagreement about which of two trees was taller and then to win the argument I called you stupid and therefore wrong. Whether you're stupid or not has nothing to do with the height of the trees. It may in fact be the case that you are stupid and made a mistake, but you could just as easily be stupid and get the right answer. In any case, the only thing that matters in this case is which tree is taller. It sounds ridiculous, but if you pay attention, you'll see this kind of thing is very common.

There are many other types of fallacies. Here are some more examples that are better than the one I just provided.

Edit: Tweaked the example based on suggestions from others.