I happen to have two hobbies, one is folk music and the other is reading sceptical and sometimes much less sceptical accounts of paranormal phenomena. I am chairman of the scientific advisory board of the German sceptics.
My personal preference by far is to keep theses two areas of knowledge separate. I'd write irate letters if my sceptics magazine would start publishing articles on folk music (except, e.g., if a claim that listening to folk music has an unusual healing power for terminal cancer is studied). This magazine here publishes everything much to my dismay but obviously to the contentment of a majority. Now I'm contributing to what I'd like not to read here but it's just too close for me to keep silent (and how often have I kept silent in those healing threads and still try to keep out of the astrology advertisement thread). Two points.
What is a sceptic?
I'm going to repeat here what has beautifully been said by grab and implicitly by others. But my impression is some of you do not read or understand what has been said in so many posts. A sceptic is definitely not a person not willing to change her mind when confronted with evidence. So the person portrayed by Little Hawk in the giraffe example is everything else but a sceptic. A sceptic avoids far out theories as long as much more easy theories are available for explanation (see Bill D pointing out Occam's razor). But when the weight of the evidence is getting larger the sceptic has to change her mind.
In my experience, the sceptic changes her mind, but the true believer never does (and often, unlike the sceptic, is unable or unwilling to say under which circumstances she would change her mind). Let's borrow Nessie from grab as an example. Grab has pointed out why the prior probability of Nessie being anything else than a hoax or an illusion is very low. But it could theoretically be proved. Stop all the water inflow and outflow and drain the lake (I hope that is not done for the sake of that beautiful region). Imagine they find a surviving dinosaur in that process. What would grab or another sceptic say? "Well, I must say, I wouldn't have believed that outcome before, but now I'm convinced. Let's get back to work and study that new species and rewrite out theories about the extinction of the dinosaurs." Imagine what the true believer would say if no species remotely similar to Nessie reports would be found. "Well, that doesn't prove it. Perhaps it is a being living in two parallel worlds, our real world and a spiritual world, only sometimes (and never to sceptics) showing in its real world form." Too far out? I haven't read that from Nessie believers yet, but I've adapted it from arguments of Bigfoot believers.
Katlaughing, your Wright brothers example seems to go into the same direction if I understand it. What would a sceptic who didn't believe in the possibility of flight have said (after the flight): Well, I've been proven wrong, so my theory that flight of this type was impossible was wrong. I've learned a lot.
Or is your point that (before the flight) there were scientists that have said it is impossible. So what? Many more have said before the flight that it is possible. Scientists have erred numerous times. Let's take the scientist Thomas Jefferson as example (the Americans know him for another achievement) who said few years before incontrovertible evidence came that stones do not fall from heaven. Or, for the British, take Lord Rutherford, a Nobel laureate, who said ten years before Hiroshima that if nuclear fission was possible at all (he was sceptical) it never would have any relevance outside of the laboratory. (Often I wish he had not erred). It also has happened that a crackpot scientist has been right for the wrong reasons. Scientists have erred often but the evidence is used as a correcting process. But with no evidence or hardly any evidence scientists will not go for extreme theories with low probabilities of being correct if other theories can explain the data much more easily.
The reliability of human observation and reports.
I have heard it so often in discussions. "You can say what you want, but I have seen it with my own eyes". The only thing I usually believe in when I hear this is in the sincerity of the person. Even very vivid memories ("I still see it like if it was today") can be wrong.
There are numerous reports and sworn oaths in the middle ages from sane persons that they have seen women flying on brooms that they have seen women giving birth to a litter of rats. People tend to see what their culture expects them to see. Reports on those women have become very scarce these days unlike reports on UFOs.
In a Dutch zoo an animal was missing and there have been over a week many sightings of that animal by reliable witnesses. It turned out later that the animal had never left the zoo when its dead body was found.
Sir Edmund Hornby, formerly Chief Justice of the Supreme Consular Court of China and Japan (surely not a person whose word is easily dismissed) has published in the 1880s a report claiming that a newspaper reporter has come into his room in the middle of the night (despite carefully closed doors) and insisted urgently on hearing the précis of a judgement to be published the next day. The judge wanted to throw him out but something in the manner of the nightly visitor held him back and so he did what the reporter wanted and said that the reporter would never be allowed in the house anymore. The man responded: "This is the last time I shall ever see you anywhere". The next day the judge found out that the reporter had died that night exactly at the time the judge had had that appearance. The wife of the judge corroborated all the facts.
It was found out later among other things that the reporter had died at daytime, that there was no judgement on the day of the death of the reporter and that Sir Hornby was not even married at that time. Sir Hornby confronted with the facts admitted they were correct and added: 'If I had not believed as I still believe, that every word of [the story] was accurate, and that my memory was to be relied upon, I should not have even told it as a personal experience."
However, usually these examples do not at all shatter the conviction of those telling me personal experiences. They only sometimes get mad at me.
There are very good reasons for scientists not to consider personal reports as evidence in the same way as they consider data from repeatable experiments.

Wolfgang