What is an example of one of these deadly heart rhythms?
In most cases, it's probably ventricular fibrillation that causes these sudden deaths from fear. Ventricular fibrillation basically causes the ventricles (lower chambers of the heart) to vibrate in a way that hampers their ability to deliver blood to the body.

What other emotional states besides fear could lead to these fatal heart rhythms?
Any strong positive or negative emotions such as happiness or sadness. There are people who have died in intercourse or in religious passion. There was a case of a golfer who hit a hole in one, turned to his partner and said, "I can die now"—and then he dropped dead. A study in Germany found an increase of sudden cardiac deaths on the days that the German soccer team was playing in the World Cup. For about seven days after the 9/11 terrorists attacks on the World Trade Center and Pentagon there was an increase of sudden cardiac death among New Yorkers.

Who is most likely to suffer from sudden death?
A predisposition to heart disease would probably increase your risk of sudden death, but it happens at all ages and can happen to otherwise healthy people.