Someone who sets out on a journey says a prayer called “the traveler's prayer”, which in Hebrew is “tefillat haderech”. It is a prayer asking God to protect us from “accidents, wild animals, bandits, and all types of calamities that befall the world.” (The entire text will be at the end of this reply.)
When our Sages composed this prayer, different methods of travel existed — e.g., travel by foot, coach or ship. Each type of travel had its own particular perils. Nevertheless, the Sages did not differentiate, composing only one version of the prayer for all the different types of travel.
The original version of this prayer for safe travel is as relevant to air travel as it is to travel by ship at sea, and therefore there's no need for a specific airplane version. So although there is a widespread custom to add a supplemental prayer for air travel, there's no requirement to do so.
Concerning cars: Someone once asked his Rabbi why, in our day, we pray for protection from “wild beasts” when traveling by car? From which “wild beasts” do we need protection? “The other drivers,” the Rabbi answered.
This prayer can be found in any Siddur, and in addition, many people keep a smaller copy of this prayer in their car and/or wallet for easy access when traveling. The text of the prayer is:
May it be Your will, God, our God and the God of our fathers, that You should lead us in peace and direct our steps in peace, and guide us in peace, and support us in peace, and cause us to reach our destination in life, joy, and peace (and if one intends to return immediately he should add: and return us in peace). Save us from every enemy and ambush, from robbers and wild beasts on the trip, and from all kinds of punishments that rage and come to the world. May You confer blessing upon the work of our hands and grant me grace, kindness, and mercy in Your eyes and in the eyes of all who see us, and bestow upon us abundant kindness and listen to the voice of our prayer, for You hear the prayers of all. Blessed are You, God, Who listens to prayer.
