We usually go for my birthday (June 8th) a few days before to a few days after and the crowds are not bad at all. In fact I wouldn't say it was crowded at all last year or the year before. We get to the park just after opening and stay until noon, go back to the room until 4 and return to the park in the evening to avoid so much of the heat, which doesn't really bother me that much at WDW, since most of the que areas are shaded or AC'd. We use the quiet pools and eat on at off times. We always take advantage of EEMH as well since the parks can be open as late as 3am as MK ususally is on my birthday
We even hit DHS on SWW and rode all our favorites in no time at all and we didn't enter the park until late afternoon, then boated over to Epcot for the evening.
Beware of the afternoon shower usually about 3:30-4 but it will cool things off a bit.
This year we are taking advantage of the 4/3 deal and going form June 6 to 13th, including a possible visit to Seaworld and one of the Disney water parks.
Suzanne