When we fly internationally, we have been using EZair to book our Business Class seats. EZair has been anywhere from 30% to 50% cheaper than any other source, including directly via the airlines. We have never had any issues with cancellations. We try to fly non-stop. If not possible, we will do one connection and always allow for at least 3 hours between flights. Our "home" airport is LAX, so we usually have many available flights/airlines.
For domestic flights, we always book thru the airline or Amex.