I trust my iPhone more than I ever imagined I would. Being slightly OCD, I have often had more than one alarm set to get up in the morning. Starting from my late teens I always had a plugged-in clock radio next to my bed, AND a battery operated small portable clock. Soon the portable clock gave way to the multi-programmable Timex watch (remember the one that was harder to program than a VCR).
It was after a year of owning an iPhone that I actually started using the alarm feature. It took me another couple months to realize I could set multiple alarms - great for those people that have varying wake-up times during the week. Simply select the time(s) that apply for the next day and you're all set to wake up properly.
Times (no pun intended) have changed and maybe I'm just not as paranoid, or maybe I just don't give a damn anymore, but I'm down to using my iPhone as my sole source for waking up. Without the alarm I'd sleep until 10AM, so I really am putting a huge amount of trust in my iPhone.