The only vitamins and supplements that should be stored in the refrigerator are essential fatty acids and those that contain food starch or biological matter such as intestinal flora. Keeping these supplements refrigerated extends their shelf life and ensures that the perishable compounds they contain will not spoil or break down.
However, you should store these and only these types of vitamins and supplements in the fridge; all others should be kept in a cool, dry, dark place. Your bathroom medicine cabinet is not a good place to store vitamins, as the humidity generated by baths and showers can cause them to lose their potency.
Your best bet is to keep them in a drawer in a bedside night table or in a kitchen cupboard. This will keep them dry and at room temperature. If you store regular vitamins in the refrigerator, you will introduce warm air to the cold bottle every time you open it. This will cause condensation inside the vitamin bottle, which increases the humidity and, in turn, causes the compounds in the pill to break down or dissolve.