Foodsafe is pretty strict about how and how long food can be stored in the fridge. At a restaurant, cooked food is rapidly chilled before being covered and put away in the cooler or fridge. (Covered warm food can stay warm even in a fridge, if covered.) On average, food are stored for 3 days. Dairy, eggs, acidic products are kept for a day or two. Dried products, such as cooked vegetable, can be kept up to 5-6 days.
At home, few of us are as diligent as the restaurants. We probably allow that pot of whatever-was-for-dinner sit there in open air until it's bed time. Then we throw it into a tuba-ware, covered or not covered, into the fridge. I know my brother would put his entire plate into the fridge, uncovered. Fridge dries out food in the fridge, so that plate of food will probably taste disgusting after 3 days. but I don't think that would stop a college student from eating it.
Is it SAFE to eat it?
Food safe tend to urr on the side of caution knowing people like me will always try to stretch the limit. My personal experience, dishes with raw food, such as sushi, is good for 2.5 days. Salmon Sushi dinner take-home on Monday is not good for dinner on Thursday, but you can probably get away eating it for lunch. It would be disgusting, but pretty safe. Cooked dishes with meat or dairy can last for quite sometime. I have gotten away with eating 4 day old chicken dish regularly, but the chicken is doused in salt, which acts as a preservative. However, egg dishes never lasts (unless it was cooked with a lot of salt). Raw eggs don't even last over night.
Can I eat my leftover if it was left out side of the fridge over night?
I have often safely ingest food left out overnight, but my kitchen is quite cool and most of my food has a lot of salt. Most food are safe. Pizza dinner leftover is safe to eat for dinner the next day, but creme blue leftover is not safe over night.
Can I tell the freshness by the appearance or smell of the food?
No. Food can go bad without showing any signs.
I microwaved my leftover, can I put it back in the fridge?
Hm... sure. But don't do it again and eat it within 3 days since it was cooked.
Here are some of my general rules for leftover food:
1. Never gamble with eggs, except with california roll.
2. After 3 days, when it doubt, throw it away.
3. Take off a day every 8 hours you leave your food outside the fridge.
4. The drier it is, the longer it lasts.
5. Salt is your friend.
6. Use my better judgement.
Good luck and always use your better judgement.