Except for this year, we always go around the 24th of June.
It is crowded, but very doable. We always go as the parks are opening (on a non EE day), get fast passes, hit the big items right away and this leaves us plenty of time to go back to the hotel for a rest/swim and then back out at night for the shows and parades. Also, we eat breakfast at the hotel, eat a good size lunch around 11:00 and a dinner around 4:30 if possible. Lots of times we just eat dinner at our hotel's food court (cheaper also). This leaves us hungry for one of the great desserts at the parks later in the evening.
That said, lines are longer for attractions, even with fast pass, it amazes me how many people wait in hour or longer lines. Return times for fast passes can be hours away, (sometimes they run out by lunch too--especially Test Track) but then you can plan your other things. Some things you can walk right in while you're waiting for your fast pass time to come around, like Hall of Presidents and big theater attractions. Sometimes I think people don't use fast passes because it means they will have to criss cross the park too many times. This is almost always true, but just take a rest in one of the seated attractions that are air conditioned. Boy take advantage of that air conditioning!
Also people get spots for parades really, really early. Good spots go over an hour before night shows and daily parades.
For a good seat at FANTASMIC-1 1/2 hours early. For Illuminations, more than an hour. Same for Spectro.
And when it's time for the mass exodus at the end of the night time shows, hold your child's hand TIGHT! It's like nothing I've ever experienced.
Have fun--we're going Easter week this year and I'm planning on following the above even more religously.
