[Android Apps and Games] dragontology:
Yeah, that would be pretty cool... but grocers, for one, have been fighting against the possibility of something like this for years. I don't think they've stepped up their game since the advent of the smartphone, or the PDA, but they haven't been challenged, either.

Here are the problems with that:

One, no grocer serves the entire United States. This could be done statewide for some, country-wide in Europe, but it would be hard to serve everybody. On the West Coast (USA), Safeway is one of the biggest chains. They're nonexistent out here. Here in NC, it's all about Food Lion, Harris-Teeter, and Lowe's Foods. Some of these are in the states around North Carolina, but they don't go very far.

Two, you have dozens of brands. There's the store brands, and then there are the national brands. Then the regionals. Milk and other quickly-perishables are regional only.

Three, prices change all the time. Officially, they change once a week on a given day, but nothing stops or bars a grocer from changing on other days.

Four, due to all this, the information would have to be crowdsourced. Kind of like GasBuddy. Cue collective groan from anybody who has ever used GasBuddy. Now for those still in the dark, I'll elucidate. Because GasBuddy is owned by no gas station, and doesn't verify information (how can it?), unscrupulous gas station owners simply log in and put false prices in. Maybe a couple cents a gallon less, but this has the immediate effect of poisoning the well -- once GasBuddy directs you to the cheapest gas in town, only to find it's the highest, and this happens once or twice, you lose faith in the service. And the more people that happens to... well, the service dies rather quickly. And you can't always fault the person who entered the data because gas prices can change daily. Maybe the person didn't intend to lie, but right after it was changed, the gas station raised the price. Maybe the gas station owner was watching GasBuddy, and as soon as the price for his station was reported, he sent his people out there to raise it. "Hey, we're now the cheapest gas station in town on GasBuddy -- raise the price by 3¢ and let's make some money off the bargain hunters."

Now, a grocery app would be less susceptible to corruption, especially in smaller states. But generally this is not something that a smartphone app is capable of handling, simply due to greedy humans being greedy.

Sorry to shoot you down, but the best way to do this is to go shopping with a partner. You're both on cell phones (don't have to be smartphones), and you both have headsets. You take a shopping list and copy it (even by hand!), and you try to organize the list by aisle order of *both* stores (so you kinda have to know them). Then what you do is, one drops the other off, and they both go into the store, on the phone, to the first item on the list. You compare the prices, over the phone, and whoever can get it cheaper, adds it to the cart. If you're the one who doesn't add it, you write the price difference on yours. You both check out, and meet up after. Later, compare lists and add the differences to see what you saved. Really helpful if you're married and you're not pressed for time. But then again, my wife and I have been married just over 6 years, and we have done this only once. (We came up with the idea of writing down and later adding differences after we did it -- I couldn't tell ya what we saved.)