Leftovers do not get thrown away because they are old. They get thrown away because the first reheating was bad, and nobody wants the second. Reheating is cooking, and the method matters as much as it did the first time.
The one question to ask
Was it crisp, or was it soft? Anything that was crisp — roast potatoes, pizza, fried chicken, pastry — needs dry heat: a hot oven, a dry pan, a grill. Anything that was soft or saucy — stew, curry, pasta with sauce, soup — is happy in a pan or a microwave with a splash of liquid. Putting crisp food in the microwave is the single most common way a good meal becomes a disappointing one.
Rice, pasta and potatoes
Rice reheats best with a tablespoon of water, covered, so it steams rather than dries. It must have been cooled fast and refrigerated within an hour of cooking — rice left out overnight is the one leftover genuinely worth being careful about. Pasta with sauce goes in a pan with a splash of water and comes back to life. Plain pasta is better fried in a little oil than reheated wet. Roast potatoes go in the hottest oven you have for ten minutes. Never the microwave.
Meat, and why it goes dry
Meat dries because reheating pushes it past the temperature it was cooked to. Reheat it low and slow, with a spoonful of stock or gravy in the pan and a lid on, and it stays close to what it was. Slicing it thin before reheating helps more than anything else — thin slices warm through in seconds, so nothing has time to overcook. Cold roast meat in a sandwich is also an entirely respectable answer.
Pizza and fried food
A dry frying pan over medium heat with a lid for the last minute: the base crisps and the cheese melts. It takes four minutes and beats the oven. Fried food goes back in a hot oven on a rack, never on a plate — anything sitting in its own steam goes soft.
The safety line
Cool leftovers quickly, refrigerate within two hours, eat within three or four days, and reheat until steaming hot all the way through rather than just warm on the outside. Reheat once. Taking the same portion in and out repeatedly is where the real risk is, which is another argument for storing food in the size you will actually eat.
Ask whether it was crisp or soft, pick dry heat or wet heat accordingly, add a spoonful of liquid to anything saucy and get it properly hot. Reheated food is only bad when it is reheated badly.