We went the first week of June in 2010. Most schools weren't out yet, so it wasn't too bad.
Memorial Day Weekend will of course be crowded, but if you can avoid that weekend you shouldn't see the crowd level get above 7.
We are traveling to WDW on May 1-8. We were told by the WDW booking agent that until the middle of June the crowds were not going to be bad. Most schools across the country aren't out yet or are just getting ready to get out the beginning of June. It sounds like we all will miss the heavy crowds & most of the extreme heat too!