I use a windup mechanical alarm clock for critical wakeups. I've had batteries fail on battery clocks, and the power go out on plugin clocks. The windup ones have never failed me.
Anecdote. A mechanical clock has dozens of moving parts, and is powered by a large, fragile, spring. I wouldn't trust it for anything critical, (which "waking up on time" isn't) but then again, I wouldn't trust any single alarm.
In response to the guy behind you: I did some googling for high-reliability alarm clocks, and didn't find anything relevant. Designing one would be amusing, in the standard vein of engineering humor. (Ha ha, isn't this horribly over-designed.) Redundant power supplies! Integral UPS! Three rad-hard microcontrollers which vote on the correct time! Two displays, in case a LED segment on one fails, and gives you the impression of the wrong time! Costs $5000, and weighs 40 pounds!
In response to the guy behind you: I did some googling for high-reliability alarm clocks, and didn't find anything relevant. Designing one would be amusing, in the standard vein of engineering humor. (Ha ha, isn't this horribly over-designed.) Redundant power supplies! Integral UPS! Three rad-hard microcontrollers which vote on the correct time! Two displays, in case a LED segment on one fails, and gives you the impression of the wrong time! Costs $5000, and weighs 40 pounds!