We go in June every trip and have been in early, mid, and late June.
When I went in early June, the first time, it was during Gay Days, went to MK on their Sat.(didn't know about GD then) MK was a zoo, very crowded, but the other parks were not crowded at all. If you avoid the Gay Days crowds (look at the website) the parks are not bad at all. We mostly go the second week of June. It is HOT and there are crowds, but not really that bad. As the month goes on the crowds get bigger.
Have a good plan: We always do EE to get things done in the morning, when it's cooler, USE fastpass, we go back to the hotel in the afternoon and swim/rest and hit another park for the night.
I have never had a bad trip in June and have never thought it was too crowded.
We like the longer hours and that there are 2 spectro parades and 2 fantasmic shows on alot of nights. We will be at WDW June 10 - 18 this year.
I don't know how the Celebration or the new packages will effect June this year, but June is my familiy's favorite time to go.
Let me know if I can help more.
Tracie