Vegetables – Are soft root vegetables edible

Pie is a good example: fruit pie tends to keep for a good while at room temperature. I have found many sites which stridently claim this not to be the case, and many grocery stores that leave their bakery pies at room temp for about three days (even psycho Mrs. Cookwell says 2 days is fine). I'm siding with the grocery stores. Nut pies tend to last longer still, because they're drier: the presence of dairy and eggs is counteracted by the higher concentration of sugar.

Likewise cake, though it can vary depending on your frosting...The more things besides fat and sugar in your frosting, the more it needs to be refrigerated. In most cases cake will stay edible longer than you'd want to eat it. Again, grocery stores only bother to refrigerate decorated cakes, or ones with cream cheese icing.

Most store bought condiments are fine at room temperature. Obviously not mayonnaise, or anything creamy, but ketchup, mustard, A-1, worstershire...They last a good long time unrefrigerated. Likewise soy sauce, fish sauce, and some of the more popular asian condiments.

I've never seen a pepper sauce (e.g. Tabasco) that needs refrigeration, and they'll last for years, though the color starts going off after a while.

There is no bacterial risk to leaving fruits and vegetables out, but this will dramatically increase the rate of spoilage. The exceptions are root vegetables, and bananas. Root vegetables will last a long time in a cool dark place, so just lump 'em in your garage if you're not going to eat them in the next week or two. And bananas will go south at the same rate regardless (though you can freeze them for future banana bread).

Fresh eggs (like, straight from the chicken) will last a couple of weeks without refrigeration (make sure they're not fertilized, or you may wake up to find baby chickens in your kitchen). The rule of thumb is "Every day unrefrigerated is like 5 days refrigerated." Once eggs are cracked, you should use them immediately.

I'd trust store bought eggs left out on the counter to eat, though its not good to let refrigerated eggs get warm again. Eggs have a wide array of natural antimicrobial tendencies, though the processing store bought eggs go through removes some of this. (citation). An easy way to test for internal contamination is to see if the egg floats in water. If it floats, toss it.

Bacon grease keeps a long time unrefrigerated, as does any sort of fat really, as long as it's strained and filtered. With fats you're more worried about them going rancid, which is a function of light and air (its a type of oxidation), so store your fat in a dark place, in a sealed container. (citation)

Butter can last several days unrefrigerated (it should be covered). I'd say as much as a week, but I have no way of knowing because it never lasts that long. It's much more likely to oxidize (see above) and go rancid than to pick up a significant bacterial colony.

It's too risky for my tastes. Cooked seafoods (fin-fish and shellfish) are nearly a perfect growth medium for bacteria, so they have a particularly short shelf-life even when properly kept refrigerated -- perhaps three days. Here is a PDF from the Texas A&M Agricultural Extension Service with some useful guidelines.