Quite simply, we store fruits and vegetables according to where they're found in the grocery store. If it comes from the refrigerator section, we store them in the fridge. If they're kept in open bins, we know they can be stored at room temperature.
Couple this with the idea that root vegetables like to be stored in the dark (since that's where they originally grew!), and it's easy to remember that things like potatoes and onions are best stored in the dark at room temperature.
There are exceptions to every rule, of course! We learned a while back that apples are best kept in a fairly cool environment. So although we find them in the open at the grocery store, we generally keep them in the crisper drawer of the fridge. Some citrus, like lemons, also does better and lasts longer when kept cool in the fridge, although they are fine kept at room temperature for shorter periods of time.
But in general, this guideline holds pretty well! Can you think of other exceptions?