Here are a few tips for making the most of your favorite recipes as well as new ones you'd like to try. Note: some of these suggestions definitely mean more work for you. If you're serious about cutting the family grocery budget, though, sacrifices must be made!
1. Does the recipe have elements that can be homemade instead of purchased? Some examples are breads, sauces, and seasoning mixes. If you have a bread machine you can make the bread you need for a small percentage of the cost of bakery breads. Sauces are better tasting and healthier when made from scratch, not to mention cheaper! Seasoning mixes tend to be mostly salt combined with common spices/herbs you already have in your spice cabinet. Try making your own, tailoring it to your family's taste.
2. Can you exchange an expensive ingredient for something cheaper? Can you leave it out altogether? One example is pancetta/proscuitto. Many Italian recipes call for these meats, but bacon/ham are much cheaper. Another alternative is going meat-free on recipes now and then. Meats tend to be expensive, so take a look at the casserole or soup or pasta dish you're making and decide if you can "beef-up" the vegetables and leave out the meat!
3. On the subject of vegetables, be sure to assess your family's favorites to find out if they're cheaper frozen, canned or fresh. In general vegetables are best for you fresh, followed by frozen, then canned. In terms of expense, it's worth it in my opinion to buy fresh even though it may cost more, depending on the vegetable. Frozen veggies are often on sale where I shop. Of course, buy what your family will eat, too! If they love green beans from the can but won't eat them fresh, by all means buy them canned -- in the reduced-sodium variety if you can find it.
I'll have more tips for you another day, but in the meantime I hope these help you to save money when you can!