Almost everyday. There are some exceptions like Grad Nights. Also on nights like MNSSHP and MVMCP the fireworks are held during the event. This would mean day guests who are not attending would not be in the park to view them. This is all at the MK.
As for Illuminations at Epcot. That would be everyday too. Unless there was something like a press event that had the park closing early. These are rare, but w/ all the changes lately there have been a handful in the last few years.