The cost for a family of four at Disney World can vary dramatically depending on how much you want to do, what you're willing to sacrifice, and when you're going to go.
Let's say you're going to go for a week. 7 nights at a value resort during value season costs $574 (+ taxes + charge for 3rd & 4th person). A 7 day base ticket for all four of you (assuming everyone is at least 10 years old) will cost $1565. Don't forget to take into account food (minimum $10 per person per meal) and your flights down and back.
There's no way for anyone here to know how you personally define "a fortune". So let's go to the opposite end of the spectrum. Family of four, 7 nights at a deluxe resort during peak season, with all the amenities. Tickets for the four of you, including the water park & park hopping options are: $1938.30. The hotel room will cost anywhere from $2373 to $14,000+, depending on what kind of room you want.
Disney offers packages for "family of four for one week for less than $1600." Read the fine print before believing that, though. They define a "family of four" to be 2 adults, one "child" and one "junior", by which they mean one kid under 3 years old and one between 3 and 9. http://disneyworld.disney.go.com/wdw/magicYourWay/magicYourWayAffordable?id=MagicYourWayAffordablePage
You may be able to get some discounts. I heartily recommend you check http://www.mousesavers.com frequently. They list discounts available to the general public, to AAA members, to teachers & police officers, and to Annual Passholders.
Another great resource is http://www.allears.net for both ticket prices and hotel rates (including dates of the seasons)
It should also be pointed out that if you're really looking to save money, you're probably going to want to forgo staying on Disney property and instead get a room at one of the nearby non-Disney hotels. Yes, you miss out on some of the theming and perks, and you'll probably have to rent a car. But it's definitely cheaper.