I've heard of many people doing things like the Food Stamp Challenge over the years. This topic just resurfaced when I saw a post on Dar's blog about her family doing a similar challenge for the month of March. Looking up SNAP (a new name for the old food stamp program) guidelines, it looks like an individual would get a maximum of $192 per month for food through this assistance program.
I think doing this sort of challenge is a good exercise in frugality but of course YMMV. Like Dar said in her overview post for this challenge, we would also be able to do this easily for several reasons--there are only two of us, we aren't busy with a bunch of kids, we don't work so have plenty of time to shop and cook, we have easy access to all kinds of food (the 99 Cent store is overflowing with cheap produce!), we can buy in bulk, and we have the facilities to easily cook meals. In fact, we usually spend less than $300 a month on food for both of us since I like to cook vegan-type foods from scratch, hubby gets lots of free restaurant meals because of his poker playing comps, and we buy big supplies of cheap food at Costco (like a giant bag of oatmeal for $7 which lasts for more than a month!).
If, however, you are looking for an interesting, educational challenge to take on, consider doing something like the food stamp challenge (or if you want to be really radical, consider the $1 a day food challenge!). Here are several resources to check out on these kinds of challenges: