We do two meals a day out, one in the room. We usually do breakfast in the room and have cereal or something else easy.
Shopping is saved until the last day (unless it is an item we know is not available anywhere else on the property). This is really helpful with kids because that way they have a chance to see what is available before choosing what they want to bring home. I know with my cousin's two DD's (mostly her 12 yo) she wants everything when she sees it, but then forgets about it an hour after they leave the store. Cutting down on impulse purchases saves a lot.
Bring your own snacks into the parks. Now I know we all like to have Mickey ice cream etc. but for things like Cookies and chips, it's cheaper to bring your own.
We also bring our own water bottles (the Brita ones).
When dining in fast food places in the parks, you can ask for meals a la carte. If the meal deal is for chicken, fries and a soda and you just want the chicken, ask for it that way. You will pay the a la carte price and not the full meal price. This adds up with a large group.
I disagree with the tip about "not eating sit down meal" however. There is a big difference between eating a meal at home and eating at a themed WDW place. However, these meals do not have to cost a fortune. Kids can usually share meals, and if you have your own water bottles, or just request water, for a drink, you can save money that way too. PLEASE try at least a few of the sit down places.

We found on our last trip (just 2 adults) that the sit down places were not all that much more than the counter places, unless you are ordering 5 course meals. Adults can share meals too. We are both light eaters and did this a few times. We weren't even really doing it for $$ sake, we just hate wasting food.