The one that offers you the best option at the best price--and there is not one that will always do that. You have to shop around. Not even the mega-search sites like Kayak and Bookingbuddy will find everything, because some of the newer low-cost airlines do not participate in those. Edit your question to add which cities you need to travel between, and you'll likely get better answers.
How to search for Nonstop flight from Oklahoma to any destination?
Check out Wikipedia for the airport you want to fly out of, they list the airlines and destinations they fly to on most of the aiports they have a website for, here's the one for Will Rogers Airport in Ok. City:
The truth is. This is really difficult. You'd probably need access to a database of upcoming flights, which will probably mean paying the government. But once you get it in the database, you just need to know a programing language to access and search it.. but i doubt either you or me will every get past trying to gain rights to view a flight schedule, months in advance... especially with all this terrorism stuff.
Your best chance is just having an input box on your site (or whereever you were going to put this) and have it link to reults on travelocity.. or Orbitz
best site for flight search with lots of variables?
I would prefer so called meta search engines and not online travel agencies. Often the search engines search online travel agencies and all their competitors. In this way you get the best overview of the prices available.
Orbitz and Expedia are travel agencies which charge a small fee everytime you book a ticket. Search engines as Momondo.com and dohop is ordinary tool like Google, which do not charge fees.
Always use several search engines to make sure you find the best price ;)