We were just there this past May from the 4th through the 9th, and despite that coinciding with the kickoff of the HCOE, crowds were very light. Most of the people who were there were at Soarin', which had just opened that Thursday.
I'm just hoping to squeeze in between two crowded times... The last half of April (Spring break) and when school lets out for summer break. I will never go to WDW again during April.. everybody and there brother was there on spring break...
I have been 6 times during the first two weeks of May. Aside from the MK being extremely crowded on Saturdays the rest of the parks are fairly easy to deal with. Once in a while you will run into a crowd at an attraction but it is generally my favortie time to go.