Eggs!

As long as eggs have not been refrigerated they really don't need it ; they'll last a month at least with just being turned every day or two (so the air gap inside doesn't dry out) and for longer term some of the old timers had lots of other tricks but can't really see needing more than a few weeks these days.

As ChromeDome says - fresh is key; ideally from the farm that they were laid at
 
..ideally from the farm that they were laid at..
And that is how it is. Free range, even.
The farmer collects the eggs and keeps them in a fridge for customers to buy.
Also all sorts of veggies and fruits, when in season.

Manned when they when can, rest of the time Self service, available early till late 7 days a week.
 
In the Med¹, the supermarket eggs aren't refrigerated, although the supermarket is usually air conditioned to below 30 degree. On the boat we put them in the fridge, mostly because we have a big fridge with space for them, but also because it can be much hotter on board at times.

If you buy eggs from the friendly farmer down the road, you should keep them in the fridge, because depending on how the chickens are kept, they may be fertilized. Those are fine to eat and you'll not know the difference, but they will not keep as long and shouldn't remain unrefrigerated for long.

¹ In Europe, supermarket eggs aren't washed, keeping the outer membrane intact and bacteria out. You should wash your hands after touching eggs. In the US, eggs are washed, clean on the outside, but this destroys the membrane, so bacteria (salmonella) may be inside, thus they must be stored refrigerated and shouldn't be consumed raw.
 
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