Mags said: "Do it after Labor Day. Cool and crisp nights, less people, beautiful days and so on."
Ditto. My wife and I hiked the JMT in September and it was wonderful. Yes, even then it's possible in some areas to find you have to walk on a bit to find a comfortable campsite, but not often, and you don't see all that many people during the day (except the last day up to Whitney and then out the Portal).
We had great weather, my 32F bag was adequate during the nights, we could have cowboy camped all along had my wife been inclined to that. Water was still not a problem. I can't speak to how hard it was to get the permit --- we applied and got it. Essentially no bugs.
This year, June might be a good time to do it, BTW. A pretty snowy experience with some creek crossing issues when I did it in June a few years ago, but this year it should be great. Somewhat of a roll of the dice as to when the Mosquitoes get active, however. In June 2008 I made it mostly through before they were much of a bother, so I presume that this year June could be buggier for JMT'ers.