I have to admit though, I'm amazed that a digital clock uses 10 Watts on a stove! I've heard of vampire electronics, but that seems excessive.
Not at all. Many draw more. The tech specs at the back of each manual will list this. If you add up the standby power (vampire power) on all your appliances, entertainment systems, computer/network systems, etc., it comes out to a surprising number.
Now add up the cost of this wasted energy that you're paying for. Look at the number for a year, for five years, for ten years. That's quite a tidy little nest egg that's being thrown out.
Worse yet, if you're in a hot climate, all the vampire power is radiated as heat. So you're using (and paying for) extra electricity for air conditioning to remove your wasted electricity. Argh!
The simple power bar with a physical switch pays for itself almost instantly, and then pays you for being smart enough to use it.
BTW, I think my last electric bill was under $80. This with a well, septic tank, electric stove, forced-air furnace, and complete home office -- in a cold climate. Good habits pay off.