Believe it or not, the day of the week you plan to visit each Walt Disney World park can greatly affect your experience. Common thought would be to avoid all weekend days, but Sunday can actually prove to be a great choice. Let's go through park by park:
We'll need to break Magic Kingdom down into two time periods: the first half of the year (January-August) when there are no holiday parties and the park is open every single night; and the second half of the year (September-December) when there are holiday parties several nights a week that cause a major shift in crowds.
Sunday proves to be the best day of the week during the non-party season, followed by Thursday. It should come as no surprise, but you'll want to avoid Saturday.
During party season, you'll want to visit on a weekday with a party. This can vary from week-to-week, so I won't recommend certain days. However I will recommend not to visit on a non-party day, except in the evening when Happily Ever After takes place. During party season I recommend picking up a Park Hopper and doing a morning & afternoon on a party day, then hopping to another park for the evening. Then do a different park on a non-party day in the morning & afternoon and hop over for Happily Ever After. Wednesday is almost always when Magic Kingdom hosts evening Extra Magic Hours, so that would probably be your best choice.
For Epcot, Wednesday and Thursday seem to be when crowds bottom out, but as you can see by the numbers, not by much. You'll definitely want to avoid Epcot on Friday evenings and all-day Saturday when the park hosts the Food & Wine Festival in the fall. Future World waits will be average, but World Showcase will be slammed with people emptying their wallets for thimbles of beer and questioning why they bought food at the Italy booth.
Disney's Hollywood Studios
The Studios see its best day smack dab in the middle on Wednesday, with both Tuesday and Thursday solid second choices. Sunday and Monday prove to be the worst. Once Galaxy's Edge (Star Wars land) opens, this chart will probably look steady every single day of the week and averages considerably higher. You've been warned.
Disney's Animal Kingdom
Animal Kingdom also sees its lowest crowds on Wednesday followed by Sunday. Just like Magic Kingdom, you'll want to avoid Saturday. The new Avatar land has proved to be more popular than expected and there are still probably lots of locals and visitors from surrounding states visiting just to check out the land.