More accurately, we tend to turn it off when it isn't needed.

In college, I never used an alarm clock for its alarm. I stared at the clock for 30 seconds before sleep, mentally visualizing the numbers it would be when I needed to wake up.
I was always awake 1-2 minutes before the time I told myself, which regularly varied over the course of weeks and months. A roommate once tested me in several ways with this as pranks -- changing the time before/after I slept, turning the alarm off, etc., and every time, I was up on time and out the door (though confusion sets when your clock insists it's 4:00 AM and you *know* you went to sleep AT 4:00am).

Nowadays, I can time the snooze button to within seconds - without looking. I wake at 30 seconds before the alarm goes off, stare at the clock till it does, then hit the snooze. Which is a 9 minute snooze... I can roll over with my back to the clock and snooze for exactly 8 minutes and 58 seconds... my arm is in motion to turn off the alarm when it goes off.

At no other point in my day am I that accurate with time (I can hit the quarter hour if I can see the sunlight, or did so within the last 2 hours, but that's it)

So is this a trained pavlovian ability of ours, or is it some uncanny ability of our subconscious?