I'm going to try to contribute an intelligent response to this thread, since it seems to be lacking them.
First, before we start arguing what is "right" and "wrong", I think we should agree on the definition of "wrong". I personally think that whether or not something is wrong mostly stems from whether someone is going to get hurt in some way. Stealing is wrong because someone loses something that belonged to them. Murder is wrong because someone else has their life taken from them. Lying is wrong because it is deceiving to others. Etc, etc... You get the point. Something being "sick" is not necessarily wrong. Drinking a glass of my own urine would definitely be considered sick by almost everyone. However, it is not "wrong". I am not hurting anyone else if I choose to do this.
Second, I'd like to separate the question into two different questions:
1. Is incest between a parent and their children wrong?
2. Is incest between a brother and sister wrong?
I will also be assuming that the sex is for pleasure only, and no children are planned. I will address that as a separate issue.
In the case of question #1, I think the answer would differ depending on the age of the children. If we're talking about underage children, then we're entering the territory of sexual child abuse. Is it possible that there could be consensual sex between a parent and underage child? Technically, yes. HOWEVER, in most cases the children are in no position to make that kind of decision and should not be exploited based on that deficiency. In many cases, this would be some degree of sexual abuse. And statistics have shown that huge percentages of the most screwed-up people (crack whores, drug addicts, people with multiple personalities) were sexually abused as children. Therefore, me must conclude that the children are or could easily be harmed as a result. Therefore, it should be considered wrong.
Now, sex between a 25 year old child and his or her mother or father would be somewhat different. In this case, the child is a fully-grown person that is fully capable of making decisions about this matter, as is the parent. I and many others would consider this situation sick. But whether it's wrong is at least debateable. Assuming they're not having kids, and they both want to do it, I don't see why it would be wrong. Nobody is getting harmed here, so despite it being very gross, I would have to say that it' not necessarily wrong.
My answer to question #2 would be similar. I personally could never think of having sex with my sister. To me, it would be unthinkable. However, whether it would be "wrong" or not is another issue. If a brother and sister both mutually wanted to have sex for pleasure, they would not be harming anyone by doing it. I can't think of a reason that it would be immoral, since there is no harm done. Sick? Yes. Immoral? Not necessarily.
NOW, to tackle the issue of incestual relationships resulting in children. The main argument given here seems to be that incest tends to increase the chances of having retarded or deformed babies. In this case, we could easily argue that the offspring would be harmed as a result. HOWEVER, if we're saying that doing something that could result in improperly developed children is wrong, then don't we have to apply that to anything that could cause this? What about people who already have some serious bioligical or genetic defects? It is possible that they may pass those traits on to their children, even with a normal sex partner. Should they not have kids? If a person has a history of health problems, or is incredibly obese, or just plain ugly, it is possible that these traits could be passed onto their children. Should they not be allowed to have children? Or should it be considered wrong? Using the "incest resulting in children with defects" argument, we may have to say "yes--it's wrong". I'm not sure I agree with this. If someone is extraordinarily ugly, or has a bad genetic makeup that causes them to have health problems, yes--they are more likely to have kids with either physical or emotional problems. But I don't think these people should be denied or even frowned upon for wanting to have kids.
I realize, however, that there is a slight kink in my last argument. And that is that people with health problems, or who are ugly, etc., don't have a choice. People faced with the choice of incest do have a choice. And I do think that complicates the issue. However, regardless of the ability to choose, the result is still the same: the children have a greater chance of being harmed as a result. So I think that whether it is right or wrong to have children out of incest is at least debateble. Plus, I would really like someone to post a link to a reliable source that shows what the harmful effects of this is. Popular opinion seems to equate the results of incest to "retardation" and "deformation". This may or may not be true. But posting a link to a reliable source would certainly help support this argument.
So, in summary, I think we need to keep in mind the difference between thinking that something is "sick" and something being morally "wrong". It's somewhat subjective, but there is definitely a difference. I think that incest is sick. I also think that someone eating their own feces is sick. But I'm not convinced that either one is wrong.
Don't flame me for being one of the few to post this opinion, I'm simply trying to be as objective as possible when dealing with this issue.