Months. Refrigerated they are good for 6months+. They may not quite taste the same after awhile but they don't go bad and can still be used for cooking. People say they age equal to 1 week in the fridge for every day on the counter at room temp so even on the counter that would make them good for nearly a month. In a cooler place than that it would be somewhere in between fridge and counter.
Some people use the water test where they put the egg in a glass of water and if it floats it's bad. I wonder though if that isn't just because the air cell gets bigger as they age and lose moisture instead of a sign they are going rotten.
Not rotten but stale. my new chicks like some I have in my fridge that are standing up but not floating. you can cook with them but if I ate eggs, I prob wouldn't eat a floater as scrambled or the like.