This morning I woke up at 7:47 and thought "what the hell time is it, my alarm should have gone off by now!" and indeed it was set for 7:30 and was turned on; it just never went off.
This happened to me once before, when I happened to wake up at 7:28 and I watched it blow past 7:30 with nary a peep.
I've never actually missed anything, but this is disturbing.
For the record, it's a Philips "full spectrum" daylight-wakeup clock. One of the round thingies.