Can you fry an arduino with nothing plugged in to it?
Although the controllers on an Arduino are pretty well protected, they can still be damaged by ESD (Electro Static Discharge). The same effect that makes a crispy sound when you pull off your woolen sweater in the winter, or after walking with rubber shoes on a carpet and you touch someone else or a metal and grounded object and you feel a pick. Static electricity can damage the controller. It may get completely broken, or it may function 'most of the time' or lifetime may be shortened.

An Arduino is also easily killed with an piezo gas lighter, just make the spark near the copper traces that feed directly in the controller. This is largely the same effect as above. 

Again, the controllers themselves are pretty well protected, don't worry too much about them. But with kids running around (on their rubber shoes) better make sure they don't accidentally draw a spark from their little finger to your Arduino. The protective metallic bag is best, but putting it away in a cupboard or box should do the trick equally well.

As a general rule of thumb, the faster the electronics, the more sensitive it is for ESD. A Due is probably more sensitive than a UNO or a MEGA. But with normal, avoiding static electricity, use you should be OK.