There isn't any single one that will do this first time, every time.
Flight search engines divide into two categories. Some, such as Expedia and Orbitz, are online travel agencies, which buy blocks of tickets from airlines at a discount and resell them.
Others are metasearch engines, which cast a wider net, scouring various OTAs and the airline websites themselves to come up with different fares and routes that fit your criteria. Standouts among the metasearch engines are Kayak, Momondo, Hipmunk, Skyscanner, Google Flights and ITA Matrix.
Each of these metasearch engines grinds in a different way, trolling through a different combination of OTAs and airlines, and no single performer takes the gold medal every time. Only by querying several will you find the rock bottom deal that applies to your particular route on the dates you plan to fly.
Each flight search engine also displays results in its own unique interface, which is why some users might consistently prefer one over all others. For example Hipmunk can display flights by their "Agony" factor – price, number of stops and flight duration, while ITA Matrix is the stripped-down bare bones. Whatever airline your search pings as having the ideal flight for you, check with the airline's own website to see if their price matches.
Buying direct from an airline gives you an added layer of security, for example, if you have to make changes to your booking.
