I have been 2 times in mid to late June and have been suprised at the small number of people, but with that said 2002 was the last time and seeing National Parks and camping has exploded in the last 5 years or so.
I do know when I go back it will be while school is in, this year it snowed last week and some of the trailes are still closed due to snow so you have to contend with that early and in the fall it can be dry and some of the animals are beeing seen less and less.
If you can stay close to Old Faithful the best time to watch it is very early in the day or very late, the crowds at mid-day are unreal.