The best time to look for airfare is EVERY DAY from the time you know that you're going until you find an acceptable price. Many of the best fares pop up and are gone within hours or days.
Most of us don't have the time to check prices every day. Fare monitoring sites are essential if you're going to find the best price. I use FareCompare.com, but there are several others. As soon as I know I'm going somewhere (or if there's somewhere I want to go), I set up an alert. When airfares drop, I get an email. If it's a good enough deal, I jump on it.
I've found airfare to Hawaii for $273, Europe for $400, and places like NYC, Orlando, LAX, etc. for $120-140. In most of those cases, the fare was only available for 24-48 hours.