Well, it depends. There is not a one-size fits all number. Every family has a different income, different tastes, and different standards of variety, health, and convenience.
That being said, I think between $500-$700 is a good starting point. Some of you may think that's ridiculously high, and some of you may think it's low. I find this amount to be challenging, yet large enough that I'm not stressed. If you are in a season where money is really tight, you can certainly make it (and eat well) on the low end of this range. It may take a little more time and effort, but it may be totally worth it to meet other financial obligations and live within your means.
*About $20 per person per week is the number I consistently read about.
I used to try and get our grocery budget super low and I ended up really stressed. I got to a point where it was not a good use of my time and energy......to shop at 4 different stores, cook everything from scratch, coupon, etc. I came to the realization that I could only go so low. We had to eat.
If you don't know where to begin or how much to budget for groceries, save your receipts for a couple of months and average how much you are spending. Give yourself some wiggle room. Budget a little more than you think you'll need. Over time, you can work on ways to reduce your grocery spending.
I find that summer food cost more than winter food. Fresh produce and grilled meats are costlier than the soups and stews I make in winter. We spend more in months with birthdays, holidays, and other special occasions. There is not a fixed number that applies to every month. Some months, my freezer is packed and other months we run out of all our staples at the same time. Having a mind set that our grocery budget is fluid and ever changing helps me adjusts with the changes that life brings.
Also, I think it's helpful to clearly define what falls under the umbrella of "grocery budget." I like to keep it clean and spend my grocery cash on just food. My grocery budget does not include diapers, toiletries, cleaners, and other household items. I order most of that stuff from Amazon. And if I have to pick up something like a household cleaner at the grocery store, I'm not afraid to run two transactions so I don't dip into my grocery cash. I go back and forth whether on not to include alcohol as a "grocery."
My biggest tip:
Meal plan. Just do it. Don't over analyze. Even a bad plan is better than no plan.
That saves me more money than anything else I do.
By the way, I don't coupon. I just don't.
A couple of good links on the subject.
How Much Should We Spend on Groceries Each Week
Family Finance: How to Save Money on Groceries
This book, Miserly Moms: Living Well on Less in a Tough Economy. I have not read it, but I heard the author interviewed and she had some awesome tips on grocery savings.