According to FareCompare L.P., the simple answer to your question is Tuesday at 3 p.m. EST. Here's why.
Airlines base ticket pricing on five variables: route competition, seat demand, route distance, seat supply, and fuel prices. Since these variables fluctuate by the hour, so do seat prices. But based on Dallas-based FareCompare's database of current and historical airfares, which it claims is one of the world's largest, pricing trends indicate that the best time to shop for airfare is Tuesday at 3 p.m. EST. That's because airlines typically kick off sales on Monday. Other airlines price match the sale, and those matched prices are live by Tuesday afternoon. Then, newly discounted airfares hit the system by 3 p.m. Further discounts are unlikely, making this the best time to buy.
Granted, there are exceptions to this general rule. But based on FareCompare's research, you've got the best chance of scoring a cheaper flight on Tuesday afternoon than at any other time during the week.