It wasn't always easy but I traveled a lot by air during my own pregnancy. What I discovered is that airlines really vary in terms of rules. Factors that influence an airline's policies and can make it more restrictive for pregnant women to travel include: how far along one is in one's pregnancy; whether one is expecting a singleton or multiples; and overall health and risks during one's pregnancy. Air travel isn't the only travel area that restricts pregnant women, even more stringent with rules is travel on a cruise ship (some start restrictions at 24 weeks!). This ties into air travel only if you are planning a babymoon - a trip before a baby arrives - since cruises are often chosen because they can be very relaxing for a pregnant mom-to-be.
What the different policies on airlines may mean as a pregnant air traveler is either having practically no restrictions until weeks before the due date, to requiring medical personnel to travel with you.
Given that policies vary, I have compiled the information from airlines based on different parts of the world.
Pregnant and Flying - In the Americas
Pregnant and Flying - Europe / Africa
Pregnant and Flying - Asia / Pacific
image courtesy of Arlene Fleming