I'd say most of May and Mid-September (NOW!) through mid-October. The weather is warm (good for swimming, water parks, night-time short wearing) but not very hot and the crowds are usually very light (this past weekend every ride was a walk-on, i.e. no wait times).
Other people may have different experiences, but these are my favorite times of year in WDW for weather and (lack of) crowds. The Sept-Oct thing gets tricky with hurricanes, though, so go mid-May if you really want to play it safe all around.