Movie Nights were first set up by Ofaloaf in the middle of September 2009, and were closely followed by Sargon setting up his own nights a couple of weeks later. They are associated with the AH.com Cinema.
Ofaloaf's nights were held every Saturday, and Sargon's currently every Sunday. Other forum members have also shown their own Movie Nights from time to time, but these two remain the most permanent and regular ones.
The thread for Ofaloaf Broadcasting can be found here on the forums, however it is no longer updated. Instead, MKN now manages the Saturday slot and has a new channel that can be found here. Shows are every other week, usually at 12:30 PST.
Both are regularly updated, and it is always a good idea to look for the most recent post in the threads that list the shows and times for the next Movie Night each holds.