Epcot Hours don't change much from day to day. They are pretty boring. All of the rest of the Walt Disney World parks change start and end times as often as Donald messes something up.
Morning at Epcot
If you a planning a trip to Epcot, you can be pretty sure that -
Future World will open at 9:00 am and close at 9:00 pm, maybe 9:30 during the busy season.
The World Showcase will open at 11:00 am and close at 9:00 pm at which time Illuminations will be shown.
Yes, a few times Disney changes just to shake up everyones vacation plans, but for the most part Epcot start and end times are pretty stable.
Oops, I almost forgot.
Extra Magic Hours
Epcot does have Extra Magic Hours. On select days the park will open an hour early, or stay open up to three hours late for Disney World Resort (hotel) guests. This is a great time to beat the crowds and ride the most popular rides without waiting in line (or at least a long line).
You can see the current Disney's Epcot Hours page there, or choose the month from the sides of the Epcot pages.
Even during the slowest times of the year it is important to have a plan to get around Epcot without standing in line. The lines at Epcot are legendary. The line at Soarin' routinely is more than an hour. The best place to find plans to help avoid lines at Epcot is at Touringplans.com. They have plans for almost every family and every time of year. Check them out.
Dad's Bottom Line
Epcot hours are the most stable hours of all the Disney World parks. Enjoy.