Call me crazy, but I like late June/early July. I love the extended hours, warm summer evenings, minimum closures/refurbs, and full evening entertainment schedule. We take a break in mid afternoon during the hottest part of the day. Crowds (except for recently) are manageable. Now the parks always seem to be crowded!
I also like spring during non spring break time, with its cooler weather, but the trade off is closures, shorter hours, and more limited evening entertainment on weekdays. The weather and smaller crowds do have their selling points, though.