Airlines normally stop allowing pregnant women to fly after they reach 36 weeks. This is done simply because of fears that you might end up giving birth in mid-air, which is not anyone would consider the most ideal birth scenario, obviously! But it is possible that some airlines will request a letter from your healthcare provider stating the length of your pregnancy and mentioning that you are in good health and there are no reasons you should not fly as soon as you start showing. There are no medical reasons not to fly during your first trimester, though you may want to think about this twice before booking your ticket. After all, the first trimester is the time you are likely to suffer from morning sickness, which is hardly the best combination with motion sickness. The passenger sitting next to you probably will not appreciate you vomiting all over his freshly dry-cleaned suit much, and the stewardess probably won't like having to clean up all the mess either.
Remind me, just why are those courtesy bags that airlines give you always made of paper? The second trimester has got to be the best time to fly, because most women feel good and are not about to give birth either. Are you planning a flight during your second trimester? Just make sure that you wear clothes that are really comfortable, and think about wearing supportive socks or panty hoses because you are a bit more likely to be struck by deep vein thrombosis during pregnancy. That is, basically, all you need to know if you are flying during this time.