Prices at Disney World are based in large measure on supply and demand. In a nutshell, times when the parks are at their least crowded are also the least expensive times to visit Disney World.
Some people will definitely want to visit when crowds and prices are at a minimum. For others, the best time to visit Disney World isn't just about the crowds; park hours and special events count, too. Keep in mind that during the least-crowded weeks, the theme parks close early; at peak times, The Magic Kingdom stays open until midnight, with extra fireworks and parades.
Below are the periods of lowest, moderate, and highest attendance. Unsurprisingly, the school year schedule is the main influence.
Most Crowded Times at Disney World
(Based on historical attendance*)
February: Presidents Week
Presidents Day is a national holiday in the US, occurring on the third Monday in February. Many schools extend the long weekend into a "Presidents Week" break.
Mid-March to Mid-April: Spring Break
"Spring Break" typically means ten days off from school for K-12 students. Dates vary, but usually fall from mid-March to mid-April. (College spring break is a very different thing...)
May: Memorial Day Weekend
The last Monday in May is is a national holiday honoring those who died in military service. It's also the kick-off for summer and a big weekend for getaways.
Mid-June through Mid-August
This is prime summer vacation time. Many kids have school holidays until Labor Day, the first Monday in September. However, in some districts, especially in the Southeast US, schools re-open earlier and crowds may ease in the last weeks of August.
November: Thanksgiving Weekend
On the fourth Thursday in November, families crisscross the country to get together, and many meet up at Disney World. Thanksgiving starts the Holiday Season; the theme parks are decorated and Disney Christmas events are on.
December: Christmas through New Year's Day
Peak season crowds are at their highest, but there are many Disney Christmas events to compensate.
Lowest Attendance, Least Crowded
January and Early February
From after New Year's Day, until just before President's Week, Disney World is relatively uncrowded.
After the kids are back to school, a more quiet period continues until just before Thanksgiving. Families with preschoolers might check for special promotions in September.
Weeks Between Thanksgiving and Christmas
Disneyphiles in the know have loved this period: Christmas decorations were up, yet crowds were less. Lately, however, it seems that more people have discovered this sweet spot.
Late February, Early March
Between high-volume Presidents Week and high-season Spring Break, crowds are less daunting.
Late April to Early June (except Memorial Day Weekend)
After Spring Break, attendance settles down until schools begin summer vacation. (Dates vary in different school districts.) Watch out, though, for Memorial Day Weekend's huge spike in May.
First Part of Thanksgiving Week
You'll be cutting it fine before the masses arrive later in the week, but Christmas decorations will probably be up and you might squeeze in some enjoyable less crowded days in theme parks that are already lit up for the holidays.
Busiest Days of the Week, for Different Theme Parks*:
Volume also varies on different days of the week. Below are some hints about busy days from a FAQ about busy times at the Disney World website.
Magic Kingdom: Monday, Thursday, and Saturday
Epcot: Tuesday and Friday
Disney's Hollywood Studios: Sunday and Wednesday
Animal Kingdom Theme Park: Monday, Tuesday and Wednesday
Also check which park has Extra Magic Hours. Each day, one or more theme parks either opens early or stays open late for guest of Disney World resorts. Theme parks tend to be more crowded on their respective "Extra Magic Hours" days.