The chances of your plane running into another plane piloted by a drunk is pretty slim in comparison.
I also have almost no fear of being in a car wreck because I still find it highly unlikely a wreck would kill or seriously injure me. I have a safe car and have lost (and regained!) control of cars plenty of times in my life without incident. Hell, I even choose to race cars in circle for fun! I only fly because I HAVE to.
Motorcycles obviously feel more dangerous to me and I have greater reservations whenever I ride one.
Ironically, I am posting this from a UA flight.
I was once on a flight that lost an engine. That was fun. We took a "normal single-engined" tour of LA, and a "normal single-engined landing" 45 minutes later. The lack of concern was both reassuring and terrifying. I expected the pilots to spin the plane on a dime and drop it back down the runway the same way we came, emergency landing, rather than keep the thing flying on one engine.
Your ability to influence outcome in a plane accident are minuscule but they do technically exist.
Here's a list of things you can do to increase your personal safety while flying:
* Sit as close as possible to an emergency exit.
* RTF(safety)M
* Know how to assume a brace position, including ideally the particular brace position which is optimal for your body shape/size in your given seat.
* If you're particularly paranoid like me, you can preemptively assume the brace position on takeoff and final approach/landing. Full disclosure: I don't have any evidence that this is beneficial and people may think you're crazy, so there's that, but it makes me feel better.
* Wear sneakers and keep them on or at least in reach at all times.
* Wear layers, preferably made from less flammable materials.
* Don't be intoxicated. I break this rule by having some drinks to ease my anxiety, but the point is to not get to anywhere near the point of incapacitation.
Even if the % of control you personally have is small, as long as it's > 0%, you feel like you're in control of the situation. In a plane, it's 0%.