It is funny to read other posts from people who were there the same time we were. Opinions can vary greatly. We were in WDW the second week of June in 2001 and the first week of June in 2002. It is a very nice time to go. In 2001 crowds were heavy but very manageable. In 2002, in was very crowded (much more than expected), but we had planned carefully and managed to get a lot done. The weather both years was VERY HUMID. The heat didn't bother us as much as the humidity. The humidity is very noticeable all day long. We did not experience much rain on either trip. In 2001, it rained pretty heavily for one afternoon, and 2 other days we had a brief afternoon shower, but that was it. In 2002, it rained one night and one saturday for about 3 hours, and one or two other very brief humidity showers. A lot of people claim that it rained all the time when they were there in June 2002, but we didn't experience it.
Hope this helps!