Argument is a science, and just like science, if you're not careful you'll end up with fudged results.  There are many methods in which falsified logical results may occur, intended or not.

One thing that is important to note is that these can appear on any side of an argument or dispute, on the side of fact or fiction, these can also show their ugly head.

These are what I find to be the five most common logical fallacies.

5. Argumentum ad Verecundiam
AKA an appeal to authority or argument from authority.  This means to use an opinion of someone who may be considered an authority figure as evidence or proof of a claim.  This comes from a misunderstanding of the concept of expert testimony.  In a court case, an expert is there to explain evidence -- his opinion alone without evidence is meaningless.  This is often combined with quote mining -- the method of taking a quote out of context to support your side.

An example would be "Stephen Hawking's favourite movie is The Wizard of Oz, therefore you will like that movie"  This says nothing to whether or not you agree with Hawking's taste in this or any other account (I actually have no idea what Stephen Hawking's favourite movie is).

In most cases, however, an expert in a specific field can be presumed likely correct on an instance.  For example, if a doctor says you have menangitis, you probably do, whether he provides you evidence as to the symptoms thereof or not.

4. Recursive or Circular Logic
Rather self-explanatory, but the recursive logic means that the clause your logic presents must be repeated infinitely backward.  Similarly, circular logic (AKA a catch-22) is self-referential and thereby backed by nothing other than the original statement.

An example of recursive logic would be, "Everything must be created, therefore God created the Universe."  This naturally leaves the question of what then, by that logic, created God.

An example of circular logic would be, "You need experience to get a job."  Given experience is having a job, the loop is endless.

3. Straw Man
This is the technique of constructing a similar, but false argument of your opponent to defeat, either consciously or mistakenly.

An example of a straw man is, "Liberals want to raise taxes, which will hurt the economy, further increasing the recession."  The problem is that this presupposes a universal increase in taxes, which is pretty much never the stance of any politician.

2. Argumentum ad ignoratium
AKA an argument from incredulity or an argument from ignorance, this is the idea that you don't understand something, therefore it's false.  What this is typically is a dismissal of something as just outright crazy without justification.

This is overwhelming in the argument against evolution, such as, "We couldn't possibly come from simple celled organisms."  Because you don't understand how doesn't say that it isn't true or even possible.

1. False Dichotemy
So simple and yet so common, a false dichotemy is the incorrect assumption that there are only two possible explanations.  This is a part of almost every argument you'll find, including but not limited to, creation/evolution, 9/11 conspiracies, climate change, abortion, and social programs.

Anthropogenic climate change is a perfect example, as it is continually a shouting match between humans are completely causing recent changes in climate to humans have no impact whatsoever.  Splitting the sides 100%/0% leaves out everything inbetween.

This methodology is also used in order to claim proof by falsification of the other.  For example, creationist/intelligent design advocates continually attack evolution as inconclusive.  This is a false dichotemy as they provide no evidence for a "creator" but suggest it's valid anyway as if should evolution hypothetically be inaccurate, the only other possibility is divinity.

Lastly, even the old videogame console wars, you'll find it.  "Red Steel sucked, therefore Wii can't do shooters."  Red Steel obviously isn't the only possible way to do a shooter on Wii.

Nomatter what you're arguing, these should all be left behind.  Making such a fallacy immediately discredits your position, whether your side could be argued validly or not.