If you ask 10 people that question, you'll get 10 different answers. Everyone has their own definition of "best." For me, best is when the parks are quietest. I'm not a fan of huge crowds. I don't like waiting in long lines. I like to feel relaxed and calm on vacation, not worrying about everything we have to skip because the parks are so crowded.
According to TouringPlans.com, the lowest crowds are:
The week after New Year's Day
End of January into the beginning of February
End of February into first week of March
End of August through the first week of October
End of October through mid November
The week after Thanksgiving through mid December
It's best to avoid all holidays or school breaks. Even just a single day holiday like Martin Luther King Jr's birthday or Columbus day will draw crowds, though not as much as full school breaks do. The marathons draw crowds as well.
Highest crowds:
Mid February (President's week)
Pretty much all of March and sometimes April (Spring Break and Easter)
Memorial Day weekend
Fourth of July
Most of June, July, and August
Thanksgiving week
Mid December through the first of the year
But some of the busier times of year are also a great time to be there, if you can handle crowds. There are all kinds of fun events going on, such as:
Marathons (February, April, and November)
Flower and Garden Festival (Spring)
Food and Wine Festival (Fall)
Mickey's Not So Scary Halloween Party (September and October)
Mickey's Very Merry Christmas Party (November and December)
When's your favorite time to go to Walt Disney World??
