I was just at the MK on Saturday, and I was mentally prepared for a real "tough" day.
I will say what the Unofficial Guides people have been preaching forever, having a good plan is much better than trying to pick a less crowded day!
And getting there early, when most vacationers won't helps exponentially as well, especially if you need to do Fantasy Land.
We were there at 7:50 or so for a public opening at 8:00 (EMH was 7am on Saturday), by 11 am, we had already ridden: Dumbo, Carroussel, Peter Pan, Snow White, Winnie the Pooh, Tea Cups (twice), waited 40 minutes to see the Fairies in Toon town, and used fastpasses obtained by me after Carroussel for Big Thunder Mountain and Splash Mountain. Later in the day we added, Pirates, Space Mountain, Tomorrowland Speedway, the Treehouse, along with Spectromagic and Wishes. We also took about a 3 hour break in the afternoon outside of the park!
All in all, it looked fairly much like our typical MK day, and we are generally used to going in May and September, definitely not April!