There is not one website that will always have the cheapest airfares all of the time. It's not possible. And there are couples of reasons. There was an articles in the past few months back that how a simple coast-to-coast flight in the US often may yield more than 25 million possible fare combinations, and that most of the searches show the top 80% or so. It is mind-boggling. To get plane tickets on any airlines one has to try as many options as possible.
One has to shop around, check the cheap airfares on all over Internet and the grab the one that you like most or fits your budget. But one has to be very careful. The major airlines are more dependable than fly by night carriers. Not only major airlines are in the business for a long time but also whenever their flight is delayed or you are bumped off, they can put you either on their next flight or transfer your plane ticket to another carrier or compensate you with the voucher to use it for next time.
Some airlines offer dirt-cheap airline tickets to promote their new flight or new destinations. So one may get better travel deals with them. Budget airlines are now offer real great bargains and one surely can save money flying with them.
Hunting for plane tickets with cheap airfares is a smart thing to do. One should always try to save as much money as one can in order to make trip much affordable and cash saved on airline tickets can be used for hotel stay or sightseeing and shopping.
To get a better start, you need to decide which cities or destinations you plan to travel between, and when you want to travel. Once those basics are established, then we can start searching and hunting fares using the right tools. If possible always be flexible in your travel dates it often helps when buying plane tickets.