This seems to be a dangerous thread to jump into (almost as dangerous as asking a groop of photographers which o-ring grease to use), but what the heck.
Let me start by saying that I have been a divemaster since 1980, and have actively worked hundreds of classes from openwater to divemaster. I started diving before I was old enough to know what fear was. I'm not saying that I am some Uberdivemaster.
Fear, and fear taken to it's extreme form being panic, are sometimes irrational and unexpected responses to stressful situations. (I am not talking phobias). I have seen a lot of divers over the years panic over something that I thought was no big deal. My gut reaction would be "what the h*ll is their problem", but then I had to put myself in their fins. What to me is no big deal is a big deal to someone else because it is new to them.
You can tell a diver that is doing the Duane for the first time that the current is ripping and not to look back for me on the current line that I will be right behind them. That to look back in the strong current can cause their mask to spin off their face. What's the first thing they do, they look back and their mask spins on their face and they panic. Why do they panic? Because they have not been trained to deal with the situation. (I have since stopped doing guided dives for people who do not have the necessary certification and experience to do a dive).
I have seen rational adults go into a full blown panic in a pool class. That person after a lot of one on one work in the pool went on to become a good diver who went all the way through rescue. Most students can be taught to deal with these fears by working with them to relax and though a lot of attention and practice.
I have had the good fortune over the years to work with an LDS, and instructors who took the ime to teach their students. If the instructor, or myself, fealt that the student was not ready for open water dives, then they did not go to the ocean until they were ready. If we fealt that they were not compitent to be certified after the prerequisit 4 open water dives, then they were not certified until we were comfortable with them in the water. I don't look at it as a certification mill where you get them in and out as fast as you can to make more money.
I have even gone as far as telling students to give up trying to dive and take up tennis or golf.
I have been in situations where I have fealt fear while diving, but it has never lead to panic. On my fist night dive I was sitting on the boat transom ready to get in the water. The instructor said "let me know if you see anything dangerous" and then shoved me in the water. He did not do this on a regular basis. I think he did it to me beacause he knew me well enough to know that I would not panic. This was back in the day when they let instructors rip your mask off under water. I'm not saying that this should be the way that instructors behave.
A while back I was diving with some friends. Upon surfacing from the last dive one of them started to have problems on ther surface. She was having trouble staying a float. Her BC had torn where the hose connects. No matter how much air she tried to add it just kept rushing out through the tear. I could see panic starting to come into her eyes. I swam over to her and removed her weight belt. She immediately relaxed. I asked her if she remembered the rule of dumping her weight belt, and she said no. Luckily, I had the experience to recognize the situation and deal with it before it lead to panic.
This is such a basic skill that we all learn in our openwater class. It's unfortunate that most divers take their openwater class doing all of the skills required to be certified. Once they have their c-card they think whew, I'll never have to remove my mask, or do a regulator recovery again. They don't realize that these are basic skills that they are taught to help them know haw to survive. These are skills that everyone should know how to do without even thinking about it.
When I first read through some of Walters post I thought that they were some what callous. After I thought about it some more I think that he is some what right. While not all panic can be completely removed, or trained away, a lot of it can be avoided/prevented by proper training and experience. We don't know what factors may lead to panic and fear in every situation. It's easy to talk about this from the safety and comfort at our computers.
I believe that the most important certification anyone can ret is rescue diver. Not because it prepares them to rescue someone, but because it teaches them their own limitations, and how to better deal with a problem when it arrises.
I am not saying that all fear and all panic can be eliminated from all divers. What I am saying is that a lot of it can be prevented by proper training in their skills, experience, and practice, practice, practice.
I have been in several situations (mostly of my own doing) that had the potential to lead to bigger problems. Fortunately, I had the proper training and experince to deal with these problems before they got out of hand. I used to tell my students, and other divers, the first rule in a crisis situation is to stop and take your own pulse. What I was telling them is what others have said here. Stop, think, then act.
If you can keep your wits, while those around you are losing theirs, then you don't fully grasp the seriousness of the situation.