As I learnt from this post, there are some fruits that should not be kept together with the others (e.g. watermelon and apple). Which fruits should be kept separately in order to prevent rotting?
Anything that outgasses ethylene should be kept away from other items (both fruits and vegetables), in a well-ventelated area, if possible.
Apples and bananas are the two most common culprits, but the list is much longer. Subzero has a list of etylene producers and ethylene sensitive items, which I'm reproducing below in case of link rot:
Ethylene producing foods
Ethylene sensitive foods
apples are typically the ones who cause problems. They cause bananas skins to ripen while the inside fruit does not actually get ripe. The best method for keeping fruit ripe without rotting is to let them ripen at room temperature, and then refrigerate them when they are at peak.
If you buy fruit in bulk, check for signs of mold/rot regularly. This way you only have to throw away the bad one, instead of having it spread to the whole batch.
I keep a list on my fridge from the June 2009 issue of Cooking Light magazine. (p. 45) Here's the details:
Keep these in the fridge:
On the countertop, away from direct sunlight in a container that allows air circulation, like a vented bowl.
And, of course, keep onions, garlic, and potatoes in a dark, well-ventilated area.