Although it sounds very similar to recent Daylight Savings Time trouble we witnessed back in November, this is much worse, we saw both repeating alarm and single alarm failures. The issue seems to be affecting iOS 4.1 and 4.0.2 as well.
Following the standard reply all of us annoyed custommers got, 9to5 Mac sayd that the bug will get fixed all by itself once the calendar hits January 3rd:
We're aware of an issue related to non repeating alarms set for January 1 or 2. Customers can set recurring alarms for those dates and all alarms will work properly beginning January 3.
What now? It's January 3rd. You know, the day you're supposed to return to work / school / life. And the day you're supposed to catch a flight you've had booked for three months and probably a day that you're supposed to accomplish lots of other tasks. Unfortunately you actually believed that your iPhone alarm would fix itself when today rolled around, but based on hordes of complaints seen on Twitter and Facebook, said fix is still hibernating. And thus, you're still sleeping. Who knows when Apple's code-apes will step up to the plate and address the issue; maybe it will be a new feature in iOS 5, alarms & DST!. In the meantime, go get a more reliable Symbian or Android device that probably won't replace your PSP and send your private data to 3rd parties, but hey, at least it will make a good smartphone!