Airplanes are as safe as you make them. Commercial air travel is extremely safe simply because the aviation industry has always been paranoid about safety. Hundreds of thousands of people in the industry are dedicated to providing for every possibility and preventing every possible mishap or accident. As a result of their efforts, flying half-way around the world in an airliner is safer than driving to the end of your street in a car.
If you flew in an airliner twice a day, starting from the time the ancient Egyptians began building the Great Pyramid up to the present day, there's still a better than even chance that you would have never experienced an accident. That's how safe commercial air travel is.
Bombs and terrorism are so rare that they aren't even significant, despite the media attention that they get. You're more likely to be struck by a meteor from outer space than you are to be involved in a terrorist attack on an airplane.
Turbulence is unpleasant and annoying, but it doesn't hurt the airplane. It won't hurt you, either, as long as you keep your seat belt fastened. It's like riding in a convertible at high speed over a bumpy road: you'd wear your seat belt then, too. Most of the time there is no turbulence, though. And the only turbulence that can crash an airplane is the kind that is found in thunderstorms … which is why airplanes never, ever fly through thunderstorms, ever (they are easy to avoid).
Pilots know about the weather at all times, because: (1) they've checked forecasts before departing; (2) ground radar provides continuous updates of weather conditions, which they can receive by radio or e-mail during flight; (3) air traffic controllers will also alert them to bad weather; (4) their operations centers will also alert them to bad weather via e-mail in flight; and (5) they have on-board radar that can detect storm activity as well. So avoiding storms is easy.
Airliners can also fly in any type of weather. They have so many instruments and computers on board that the pilots can fly to their destination and land even if the windows are painted over—they can conduct the entire flight using just the instruments on the flight deck. And in poor visibility, on-board computers can land the airplane automatically, with the pilots merely supervising. Modern navigation systems are so accurate that they can tell if the pilot strays from the centerline on the taxiway on the way to the runway.
Just about everything on an airplane has back-ups. There are multiple engines, multiple generators, multiple electrical systems, multiple batteries, multiple fuel tanks, multiple hydraulic systems, multiple pneumatic systems, multiple everything. People who are paranoid about safety have thought of everything. They've even thought of things that you haven't imagined yet, and they've provided for them.
Airplanes are also extraordinarily well maintained. If your car were maintained as well as airplanes are maintained, you'd be able to drive the same car every day for your entire lifetime, and you'd never even get so much as a flat tire.
You're more likely to be killed crossing the street at the airport to get to the departure terminal than you are to be killed during an airplane flight.