Over the years I've found that American Airlines has some really great fare sales. The are very stong in the European, Caribbean and Central American markets. While they don't have a lot of flights that go to Asia or Africa or South America, they have a very strong code share program. They reguarly have sales. Plus, they have a good air miles program and are very strong all over the U.S. Their Dallas hub has international flights which depart to a large number of countries, making it nice for those of us who live close to Dallas.
Air France has some good promotions. They don't fly from and to a lot of places, but they can be a really good source of travel deals. Plus, their web site is very easy to use and the odds are that you won't spend a lot of time searching needlessly for the one seat left at the sale price. They show prices by date for their promotions. What this means is that you won't have to spend hours and hours trying to find a good deal. The bad news is that Air France doesn't fly from or to as many locations in the U.S. as some other carriers.
Air Asia is one of my favorite carriers. The reason is simple - they are incredibly cost effective. When I am in Asia, they are my carrier of choice. Sometimes, I fly with them half a dozen or more times a year. Yes, booking can be a headache. I have problems with American credit cards being accepted easily by their computer system. They are often late taking off for departure airports. Refunds are merely a wish. Lots of people complain about them. But, when I'm in Asia and I want to go somewhere, I check with them first. Their average cost per mile is incredibly low. On the day I grabbed the jpg from their web site they were offering round trip base fares to London or Paris from Kuala Lumpur for about $650. That's a good deal. Some of their local sales are often surprisingly low. When I go to Asia I can fly all over the continent with them for $30 to $100 a flight.
When I copied the jpg from the Ryan Air website they were promoting base fares from London to Cork, Dublin and Frankfurt for $15. I can remember flying ryan Air from London to Venice, Italy once for the full fare of $40. When I go to Europe, this is the airline I look at first for fare information. Yes, they can be a pain, but at least they are a cheap one. People tell me there are other carriers in Europe that are just as cheap and, operationally, even better.
Easyjet flys all over Europe. People tell me they do it well. The thing I like best about them is their "year view" which shows the best prices for flying during the year. Want to know the best current price for flying between two points for the next year? It's a click away. That's hard to beat. I sometimes wish we had airlines as good as Air Asia, Ryan air and easyjet in the United States.