I think we're always trying to keep our food fresh so we always want to keep it in the refrigerator. There are however foods that don't benefit from the cold.
Bananas - Don't ripe well inside the refrigerator so it's best to keep them out.
Tomatoes - Don't really taste as good if they've been regrigerated so I find that keeping them out is better if you want good tasting tomatoes. . Sweet Potatoes - When exposed to cold temperatures, starches found in potatoes will turn to sugar, disrupting their flavor and texture, not to mention increasing their sugar content. If you prefer tasteless potatoes that cause weight gain, then go ahead and refrigerate.
Apples - They loose their flavor and texture when refrigerated so it's best to only put them in for 30 min. before eating if you like a cold apple.
Onions- Tend to become soggy and they also make the rest of the food smell like onions.
Avocados - Much like the banana, refrigeration shuts down an avocado's ripening enzymes.
Coffee - Contrary to popular belief, coffee is best stored at room temperature to allow the natural oils within the coffee bean to activate its pungent aromatic scent.
I'm sure there might be other food that is best stored at room temperature but for now these are the most common ones.
