2011 started with this same problem for iOS users where alarm clocks on their iPhones wouldn't ring when the New Year rolled around. The problem is a result of iOS 4.2.1 which back then affected users who freshly bought the iPhone 4 or updated their iPhone 3Gs to iOS 4. According to Engadget, most users should not have this problem anymore, as there is a way out. The simple way being to upgrade your phone's OS to iOS 5. Come on, it's about time. Make it a New Year's Resolution.
Update your iOSes already, sleepyheads
People with original iPhones, of course, don't have to worry about the problem, but folks with iPhone 3Gs and the second generation iPhone Touch are sadly stuck in their predicament. iOS 4.2.1 is the highest they can go. However, try deleting each alarm and adding them again. That should fix the problem. If not, let us know in the comments section below.
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