This article is from the Problem Behaviors in Cats FAQ, posted to rec.pets.cats newsgroup. Maintained by Cindy Tittle Moore with numerous contributions by others.
The best way to discourage running to the door is never to let the cat succeed! After a history of unsuccessful attempts, the cat will stop trying. After even one success, the cat will try hard and for a long time.
Tip: don't arrive at the door with three bags of groceries in hand and expect you'll be able to keep the cat in. Instead, put down all but one bag and use that bag to block the floor level when you come in. After you're in, bring in the rest. In general, spend the time to be in control whenever the outside door is opened. Kids will need to learn how to keep the cat in too. A waterbottle may help with persistent cats. It will pay off later when the cat stops trying to get out.
To turn a formerly outdoor cat into an indoor one (or to discourage a persistent one, you might try this, recommended by the San Francisco SPCA: Enlist the help of a friend to hide outside the door with a hose and spray attachment and have her or him spray the cat when you let it out. This may take several applications, over several days.
Some cats are remarkably persistent, and never seem to give up.