Are we talking about what you fear is going to happen while flying, or the sudden realization of what just happened? There is a difference!
The fear of what is going to (or could) happen will recede as your experience grows, as with increased experience, fewer things should seem to be out of the ordinary. Or at least as far out of the ordinary.... However, a good dose of fear is a useful life saver, and should never be ignored! Ideally, your fear causing you to not do something, will shift to your wisdom causing you not to do it!
Fear of what just happened is quite different.... It gets you some time later, when the whole picture sinks in, and you realize how close you came. I have had that a few too many times (including the only time I have ever damaged an aircraft - while hand propping one).
Those are the ones you must recall, and share, in the hope that others learn before they do it too! It is a certainty that I have the proverbial angle on my shoulder, for all the things I have gotten away with in airplanes, which I should never have. The best I can do is to remind others why they may not be so lucky, and approach with great caution!
Things I remember most, which scared me after that fact.....
I was a 16 year old passenger in a Cessna 150, at night, over the cloud, with airframe ice, which the pilot spun.
I was the pilot of a Cessna 303 (fully deice equipped) which had a factory design flaw (later corrected by AD) and in icing conditons, it tried to swap ends at cruise speed, and worsened when I slowed down.
I was the co pilot of a Twin Otter over the south of France in August, falling out of control because of airframe ice
'seems to be a theme there...
I was the pilot of a Cessna 180 floatplane, which had a flap track separeate on a water touch and go, and the flaps jammed at 20 degrees.
I was the pilot of a Cessna 206 with a trim rigging error, which required an estimated 50 pound push to maintain level flight
I was the pilot of a Cessna 185 floatplane with a rudder system mis-installation, which caused it to want to sawp ends at any speed
Another theme...
I guess I'd say I'm afraid of unmanagable icing encounters, and control system failures. In each of the afore mentioned situations, I had enough time to ask myself "is this the flight which is going to kill me?" (though with the C 206, not much time!)
On the other hand, two weeks ago, I did a series of flight test spins in a Cessna Grand Caravan with an external load. I feared doing it somewhat, but it was all planned and briefed, and ultimately not scary at all! I later mathed out the maximum rate of descent - 9200 FPM!
It is wise to always have some fear, but make sure it's informed fear, and properly managed...