Yes, there is a "Screening Room" on the Explorer. Unless you have a Grand suite or better, you won't have a DVD player. You will have a television and there are movies. I travel with a 10 inch portable DVD player and bring along about 4 movies. I have never watched a movie while aboard a ship, but I do when in an airport or on the plane.
Thanks Sonny, I asked this question to someone who had been on the EOS and they told me no there wasn't. Nice to know, of course I'm not sure when there will be time to "see a movie". Is there a listing in the room as to times and titles of what's playing? How many people does the screening room hold?