Most families have a lot of movies, most of which only occasionally get watched. Rather than buy or rent others, arrange with another family to trade movies around regularly.
Keeping track of who owns what can take some work. You can stick a mailing label on the boxes to keep track of who owns what, and keep a list of who has borrowed what so that you know where particular movies have gone.
This of course takes a lot of trust, but it greatly cuts down on the need to buy or rent movies. Just beware of special favorites of the kids. Tempting as it may be to get rid of that movie that is requested 200 times a day, even for a short time, some movies should be loaned out only once the kids are sufficiently tired of them to share well.
Then again, the movie can always go overÂ to have the kids watch them together.