There's better advice here than thinking about the odds of a crash, but if that helps, you could also factor in the odds of actually dying in a crash - not just being in one - because that's even rarer.
I was on a plane that experienced an "uncontained, catastrophic turbine engine failure" (Delta 1288) that killed two people a few rows behind me. It was traumatic, and I rented a car and drove home instead of flying, but it wasn't long before I was regularly flying again. Physically, I was completely unharmed, and I got to experience safely leaving a plane through an over-the-wing exit. I learned that even in a worst-case scenario, people can and do survive.
That must have been terrifying. Can you talk more about what happened between the moment the engine failed and the plane landed safely? How long did it take? Did the captain communicate with passengers frequently? How about flight attendants? What went through your mind? I'm nervous about flying and knowing what happens in this scenario may help me prepare.
The plane didn't leave the ground - the engine blew up as we were accelerating for takeoff. That's now something I now find reassuring: takeoff seems to be a time of maximum stress on the engines - if they're going to break (or explode), hopefully it will be before the plane leaves the ground!
This was 20+ years ago now, but I remember being awed by the performance of the pilots and flight attendants. The plane braked hard right after the explosion, so the pilots clearly noticed it and took immediate action, even though I heard later that people in first class were so far away they didn't initially know why takeoff was aborted. In the moments that followed, one pilot was giving first aid and I saw him run down the aisle - blood on his hands and shirt - to get more help and medical supplies. Yet he was calm and professional throughout.
Some people yelled to "stay calm" or "don't panic", and people listened. Announcements were clear when there was no further danger and how we were to exit.
We were kind of dumped in the terminal at the end of it all, though. I remember an announcement that there were no additional flights that day, so we couldn't get rescheduled until tomorrow. Seriously? There were ambulances, news vans, and Red Cross vans at the terminal almost immediately. The airport was clearly completely closed down - I don't know for how long. And no baggage claim, of course: it took about a week to get our luggage back.
In the weeks that followed, the FAA sent a questionnaire that was extremely detailed. They wanted essays about every aspect of the flight and it took a long time to complete.
A couple of years later, I was on a cruise and met a young pilot who'd just got his first job with an airline. I mentioned this experience, and he said, "No kidding! We totally studied that accident in school!" I find that very reassuring... aviation seems to learn from mistakes and experience better than any industry I've worked in.
>takeoff seems to be a time of maximum stress on the engines
This is true, 'band A' throttle is used for takeoff and the first minutes of flight. Perhaps a pilot could chime in here, but I don't think there's any other non-emergency situation that band A would be used in flight.
It's also why jet engines are overhauled on a takeoff schedule. ie some parts have a lifetime of 20,000 cycles (takeoffs/aborted landings)
I was on a plane that experienced an "uncontained, catastrophic turbine engine failure" (Delta 1288) that killed two people a few rows behind me. It was traumatic, and I rented a car and drove home instead of flying, but it wasn't long before I was regularly flying again. Physically, I was completely unharmed, and I got to experience safely leaving a plane through an over-the-wing exit. I learned that even in a worst-case scenario, people can and do survive.