When to toss Leftovers?

"Leftovers make you feel good twice. First, when you put it away, you feel thrifty and intelligent: ‘I’m saving food!’ Then a month later when blue hair is growing out of the ham, and you throw it away, you feel really intelligent: ‘I’m saving my life!’"
– George Carlin

Question: "When do I throw out leftovers"?

TasteOfHome.com has a simple answer, "If in doubt - throw it out". 

Don't rely on taste or smell or looks. Food may contain an unhealthy level of bacteria yet give no clue after several days.

A more detailed answer is, "it is best to eat leftovers within 2 days. Some items may still be safe after 3-5 days."

Raw foods from potentially dirty environments have a higher risk of contamination. These include fresh poultry & fish & other seafood (shrimp, scallops, squid, and shucked clams, mussels, and oysters). Don't keep these items in a fridge for more than a day (two at most).  Fresh (raw) ground meat and chopped meat (stew chunks) are equally at risk with more surface area exposed for bacteria growth.

Cooked foods will usually keep for 3 days (5 at most).

There are some foods that are are designed/created for a slightly longer shelf life:
hard cheese: 3 to 4 weeks
soft cheese: 1 week
yogurt: 1 - 2 weeks

Advice for Storing Leftovers

Begin with a clean container with an airtight seal. For items still hot, use shallow containers or divide the food into smaller portions so the center of the leftover can cool quickly. Some experts suggest waiting until steam has stopped rising from food before putting it into the refrigerator so that you don’t heat up your refrigerator. But don't wait too long.

"If food has been left out for longer than 2 hours, don’t put it back in the refrigerator, and don’t keep it for later. It’s not safe to eat." - TasteOfHome

"If food is left at room temperature for more than two hours, (one hour in hot weather) bacteria can grow to harmful levels, making it unsafe to eat." - European Food Information Council

Other experts discourage cooling leftovers on the kitchen counter but instead recommend putting warm leftovers quickly in the fridge. Bacteria are like Golilocks and love warm food (not too cold and not too hot) and grow quickly at a temperature that's "just right". My mother is a stickler when it comes to food safety. My wife & I were surprised when she took the hot bucket of Kentucky Fried Chicken we had purchased for a picnic, transfered it to tupperware, and then put that in a cooler with ice, because it would take us a few hours to reach the picnic site.

P.S.
The quote at top comes from a George Carlin routine called Ice Box Man which I recommend.