Hi it's happened to me today, for the first time! It annoys me that this is an ongoing problem since 2008 and apple are so useless that they can't answer this simple tech question! My problem has coincided with daylight savings time and my alarm is going off an hour late. I really need a fix asap!
Are you located in Europe by chance? If so, your issue might be a little different. Over the weekend, people reported that there was some DST glitch with the alarm clock not going off/going off an hour late. AppleInsider says that this DST alarm clock glitch might be fixed in the iOS 4.2 update (November).
Back when I joined this thread in 2009, the alarm on my 3G would just sporadically not go off. Shortly after my post, I guess it kind of resolved itself, I don't know. Also, since then I've bumped up to the iPhone 4 and (fortunately) haven't seen this issue yet.
V 4.1 iPhone 4
I'm near London, England.
The problem started when the clocks went back an hour at the weekend. Like many others, it seems to ignore alarms with repeats. When I set it to got off adhoc, it seems to work. I'm gonna try manually setting the time on the phone to see if that helps. I wonder whether the Internet clock caused the issue when it set the time back an hour.