I have to agree with the postings so far....September. My wife and I have gone in September 9 out of 10 years. We had to change to May 1 year as we were "expecting". Our experience in May was good, but something we didn't consider was less cloud cover meant more sunburn potential even thought the temps were a bit cooler.
Our reasoning for September is primarilly that it's an off-peak season. We don't have to make many Priority Seatings until we get there and decide where to eat the day before. Many places we could just walk in. Parks are slow and lines are short. We stay an average of 8 days, so the leisurely pace is great and makes it easy to squeeze lots more in! Also, we've been there for the start of many new celebrations as they tend to start in off-peak so they can roll everything out. We book our trips before the celebrations are typically announced and it just seem to work in our favor.
You do need to be aware of the weather. September is the ramp-down month for the hurricanes. Of our 10 years going, 1 year it rained about 50% of the time and was cool do to cloud cover. 1 year we arrived 1 week after a hurricane and left 2 days before they actually closed the parks (only twice in history as I recall) so we got lucky. The other times, hot, humid, typical afternoon rains, but otherwise very reasonable!
This year we are staying 10 days, last week of Sep through first week of Oct. Lots to see this year with Mickey's Not So Scary.., Food & Wine Festival, and the EPCOT celebration, so we'll need everyday. Hurray for off-peak seasons!