This is tricky, since every location and season will cause this to vary a bit. In general, according to this article, the average best time is 70 days out. In the article they break down more details by season and location too.
One thing I know first hand though, airfare is NOT like hotel rooms, you want to book in advance for the best deals. It's rare that they will drop their ticket prices the night before since they assume most people are in urgent need at that point. I've found a good bit of luck two weeks out though.