Chemical compounds should change after re-cook. Some formation can be harmful. There are 7 types of foods mentioned here which should not re-cook.
It is highly unsafe to re-cook spinach. Eat spinach as soon as possible after cook. Reason is spinach contains Nitrate compounds. When you re-cook, these Nitrates forms poisonous Nitrites.
Celery
This is also a type of leaves which contains Nitrate compounds and also act as spinach.
Beet Root
Beet Roots contains nitrate compounds which could form nitrite compounds when re-cook.
Potatoes
People in the world consume large amount of potatoes. And it is highly nutritious. If you usually cook potatoes for the second or third time also please stop it immediately. The chemical formations when re-cook will be harmful.
Eggs
Boiled or fried eggs are also harmful when re-cooked. And sometimes can be deadly. Do not ever do it.
Chicken
Do not cook, previously cooked chicken again. That can make digestion problems. Reason for this is protein structure change. When cook chicken do not use high flame. It also cause to protein structure change. When using small flame it increase the cooking time but it is so safe.
Mushrooms
It is highly harmful to re-cook mushrooms. When use later it is safe to eat on room temperature or cooled. Digestion or heart problems can occur if you re-cook mushrooms.
So keep those in mind when you prepare foods.