Disney attendance numbers vary throughout the year and are unpredictable, but the below is an indication. Holiday periods are always busiest with weekends being particularly so with both tourists and locals visiting the parks.

Normal trading periods can vary too but the parks tend to be busiest on the below:
Magic Kingdom Park: Monday, Thursday, and Saturday
Epcot: Tuesday and Friday
Disney's Hollywood Studios: Sunday and Wednesday
Disney's Animal Kingdom Theme Park: Monday, Tuesday and Wednesday

Highest Attendance
Christmas Period
Mid March to end April
Mid June to start September
Thanksgiving Day and Weekend following

Moderate Attendance
End February to early March
Late April to early June
Early Thanksgiving week

Low Attendance
January to Presidents Week in February
Mid September to Thanksgiving week (early October)
Week after Thanksgiving (early October) to week before Christmas