Travelling during pregnancy can be a risky proposition. There are recommendations depending on which trimester you are in. Each trimester has its own concerns to be considered.
First Trimester:
The main issues within the first three months of pregnancy revolve around possible miscarriages. The recommendation to not announce your pregnancy during the first three months stems from the fact that most miscarriages occur in the first trimester. Any thing that may encourage stress or anxiety is generally discouraged for newly pregnant mothers. Also the nausea and sickness that usually happens during the first trimester may be inconvenient for flying.
Second Trimester:
These are typically the best months to fly. The risk of miscarriage has mostly passed and premature labor is not yet a concern. Unless there is a medical condition or other issue, flying during the middle three months of pregnancy should not pose a problem.
Third Trimester:
Not only are the last three months uncomfortable, the risks of premature labor are heightened. In fact, doctors recommend not flying in the last trimester and most airlines refuse to allow women who are 34 weeks pregnant to fly at all. Of course, sometimes this can be avoided with a certificate from a doctor.