How can I know how long home-cooked food will stay good in fridge? As through the week we too busy to cook we have gotten the idea of cooking a big bunch of food in the weekend, storing it in the fridge and eat it later in the week.

I am a bit concerned how long things will stay good in the fridge. For example mashed potatoes (which is prepared with milk), minced meat steaks or a cream-based sauce.

Are there any general rules of thumb that can be used to estimate how long things will stay good? And are there any 'dangerous' foods, foods that can be spoiled but not show any mold or smell strange, but are not good to eat?
The USDA says to eat refrigerated leftovers within 4 days.

Be aware that how long you leave something out before refrigeration and the size of the container can shorten the edible lifetime. The gist is the longer it's warm, the more [likely] pathogens will be able to multiply to unsafe levels. A large container holds heat longer and takes longer to reach 40°F.

There's also some other interesting information on the linked page about safe storage durations for many store-bought items as well, including recommendations for how long it will stay good in the freezer. To be fair to @Allison's answer, many of the durations listed in that chart are 3-4 days or 3-5 days, though some are longer or shorter.