You do realise that even without the obvious looting which would happen in such circumstances your average supermarket would be empty within 48 hours if it did not get its daily deliveries. So, if deliveries had stopped and and people were looting them they would probably be empty within 4-6 hours of the apocalypse.
Even the massive supermarket supply warehouses which are dotted around the country only hold a few days supply of most non-perishable foods (e.g. tins/packets etc). They have gone to great lengths to reduce the cost of stock in their supply chain.
I don't think it would be very long at all until things turned nasty
Like I said, I'm basing it on what kind of Apocalypse we are talking about.
If we were talking about some kind of event that happened which kept the majority of the world alive, then I can fully see why you would get widespread looting and fighting.
However, if we are talking more along the lines of small pockets of people, where there is hardly anyone around, I don't see why people would necessarily want to kill one another when for the meantime, there would be enough food in places such as supermarkets to go around.
Images that come to my head are films/books like 'The Road' where you've got people trying to scavenge cans of food, it's only as that's got less and less that people have turned to killing or eating one another.
Or '28 Days Later' where there were zombies. There were few people, but plenty of food to go around, I see no reason why people wouldn't work together and it's only when food becomes scarce that problems arise.
Or 'Threads' the BBC Cold War film looking at a Nuclear strike on Sheffield. It was only after years and years off lack of sunlight and the ability go grow food that people really turned to prehistoric times and started killing each other.
I think there's an element of needing to survive, but to start outright killing people for no real reason is making you less and less a human being.
Also, I'd argue that when not behind your keyboard, if you really were in a situation where you held up a supermarket full of looters, would you honestly really shoot them all, baring in mind they are all just in need of food like you.