That very much depends on your fridge temp and how many times it's getting opened per day. Note: the meat (whole carcasses) that are hung behind the counter in the walk-in fridge in your butcher or supermarket are kept many, many days, simply because there is less temp fluctuation.
Before finishing the renovation on our home, we used a galley kitchen (with tiny fridge) whilst storing all the main food items in the large refrigerator on another floor. At the time, I only opened that refrigerator to re-stock the smaller fridge in the galley kitchen.
You know....the veggies lasted soooo much longer. Cheese and butter and meat all kept better.
Now that I am constantly opening that refrigerator all day as opposed to once every 3 days, my food does not last near as long.
I generally go by the 3-day rule as well though I'm changing my ways, since I think this is often paranoia at work, while maybe some bacteria especially fermentation is healthy. Another thing I've noticed is when I do natural fermentation it does not stop when it goes in the fridge. Each time I open the jar I still hear that frizz from additional fermentation. I haven't had time to look into this but I leaves me with a few doubts about exactly what is going on behind that refrigerator door.
I'm sure the shelf life of cooked food would depend a lot on what else is in it: salt, oil, sugar, vinegar (preservatives)