ITA is the best free flight search engine on the Internet. Understanding all the nuances of ITA can be very difficult and requires practice, but the result can be rewarding. The biggest problem is that ITA only tells you that a fare exists. You will need to find it on your own, and for that I usually move on to Kayak or Hipmunk. There is also a second version of ITA Matrix that will order results by price per mile (PPM).
Kayak and Hipmunk
These are meta search engines, which means when you search with one of them they will go out and search with multiple sites, presenting you with the combined results. This reduces the risk of incomplete results from any one site. Kayak and Hipmunk don’t sell tickets themselves, but they will provide links to other sites that do (like the airlines or Orbitz). I don’t like to start with them because ITA is more powerful, but they are good enough for casual travelers.
Unlike Google Hotel Finder, Google Flights loads search results very quickly and works better, as long as you’re wiling to give up some of the customizations available from ITA, Kayak, and Hipmunk. If all you want is the cheapest possible option for a simple round trip or one way, Google will work and can also tell you which day to travel. However, I find that the list view is relatively uninformative when choosing among your options.
Orbitz, Expedia, and Travelocity
These online travel agencies (OTAs) sell a lot of the same tickets that you could buy direct from the airline, and usually the airline has the lowest price, too. So why buy from an OTA? First, you may want a mixed itinerary with multiple airlines from different alliances. Second, tricked fares almost always require booking through an OTA. Finally, OTAs sometimes offer promotions or rebates through websites like BigCrumbs. However, using OTAs may complicate fixing an itinerary when flights are changed or cancelled.
Hotwire and Priceline
These sites offer cheaper fares than other OTAs, but the catch is you won’t have as much control over which airline you fly or what times you travel. Personally I have never used their services because convenience and comfort are almost as important to me as price, even on a mileage run.