Traveling in pregnancy is safe as long as you take certain precautions.
When commercial air flights began there were concerns about air-pressure changes inside the cabins and exposure to radiation at high altitudes. Nowadays, cabin pressure in commercial airplanes doesn't change that much, and exposure to radiation is less of a concern.
The American College of Obstetricians and Gynecologists (ACOG) says that air travel won't harm a pregnant woman or her fetus, and doesn't discourage women from flying. ACOG suggests to not fly after 36 weeks of the pregnancy because of the increased risk of going into labor as you approach your due date.
There are certain precautions you should take when flying, especially if it's a long flight: