What kind of flexibility do you want?
One movie sent simultaneously to all TVs or allowing each TV to decide what to watch when they want to watch it?
Sending a video signal via RG6 or HDMI will get you one program (two if you run a dual system) into every TV.
To allow the people to watch what you want, when you want, you would be talking setting up a video server onto a network (wired or wireless, I would think that wired is better) and have a network player in each room.
I haven't started looking seriously at this yet but know that some of the PVR software will work that way, using a local processor to display the video that is recorded (including TV programs via a receiver card in the server) on a local display. I was hoping that a very minimal (footprint) computer could be set up with that really only needs the screen display and a pointing device to access the menus for the video system (OK, and a keyboard when you want to check email from that room). I don't know but expect that there will be some sort of premade receiver for this available that is less flexible and smaller than a computer.
I did happen to see an ad for a TV recently
that had a wireless network connection for receiving video from a server built into it. I was thinking that this could lead to a server and possibly the network receivers to put next to non-wireless TVs.