With very few airplane crashes recorded every year out of the tens of thousands of flights taken I would say that airplane travel is one of the safest travels of all modes of transportation, airplanes are designed at every angle around safety and in the event of something going wrong there are procedures and methods in place to protect the passengers.
Yes, airplanes are safe. The companies like Airbus and Boeing put safety as their number one priority. Those huge airliners are over-engineered on purpose so that a lot of things can happen to them and they'll still keep flying. Once purchased, that safety depends on the airline doing proper maintenance.
Airplanes are the safest method of travel by far. The news always reports plane crashes which is why we hear about them so much, but from a statistical perspective they are much safer than any other mode of transportation. You are much more likely to get in an accident on a car or in a train than on a plane.
Air planes are designed and built by the best engineers in the world, and are routinely maintained by the best mechanics in the world. Very rarely they crash and, the truth of the matter is, is that most do not die on impact. If you follow the instructions, chances are that you will live through a crash.
Airplanes, just like any other form of transportation, have risks associated with them. However, traveling in an airplane is in fact safer than many other forms of transportation, including driving in a car. Just because there are risks with air travel does not mean that it is completely unsafe. Nothing in this world is completely safe.