For domestic, I usually book 1-2 months ahead when on award. There's usually some availability if you're somewhat flexible with dates/carrier/cabin class.

For international trips, I did one last year when I booked 3 months before (in economy) and another one (I think 6 months, again in economy) ahead of time (as you gathered, there are usually seats if you don't care as much that it's in coach for a long haul...) I have also booked a one-way segment in F on another carrier on an international segment when my original travel plans fell through, due to a strike. That was pieced together literally two days prior to the flight, but of course, I got dinged with the close-in award fees (which evens out the baggage fee I would have to pay otherwise, anyway)

I have an upcoming trip in J, and this is the only one I've ever booked roughly 300 days out (only because it's for a party of 5). And even then, not everything was where I wanted it due to availability when I booked it. It required monitoring and tweaking once award availability opens up. The worst part - to me - about booking so far is advance is that it's quite a wait until the actual trip.