in late september and we had the vacation of dreams.....major rides were walkons such as thunder/splash mountain,space mountain etc! and nice temps in mid 80's........although we took our kids out of school for a week, my older son was given homework to do so he wouldn't miss too much..........i think he learned a lot on his trip! 
). All parades are running, the staff is beefed up, it's great! We have never gone back to the hotel to take a rest. Sit down for a while at the park if you need to, but you should not have to go to your hotel to get out of the sun. As for the crowds, they may be higher in June, but to me, that's part of being at Disney. I enjoy seeing that others are having as great a time as I am. It is still manageble. Just plan your schedule before you go, utilize every second, and you'll be just fine. Have a great time. We're going back in June of '07!!!! 

Mandabella said:We did May 28th through June 5th last year. I honestly didn't think it was that bad. It was definitely more crowded than our usual trips in the off season (late October/early December), but attractions were still doable. The only thing that got annoying is that there was thunderstorms practically everyday that lasted for hours. It was a good thing we brought a 2nd pair of sneakers.
Oh and Pleasure Island was packed because of Gay Days, but it was sooooo much fun!!!
I'd go again during that time period.
We were there in early June last year & the year before. In 2004, it was the first week in June & SO HOT, SO CROWDED!!! Of course we still had a blast but you really have to prepare.
