I'm having a similar problem. The weird thing is that the clock/weather widget is still appearing, but the clock app seems to have mysteriously disappeared. When I try to click on the clock, which would normally take me to the alarms/world clock etc., it doesn't respond and Clock is no longer in my app list. What do I do?
I'm having the same problem. Last night I modified and enabled a couple alarms, but later I noticed the alarm icon was missing from the notification bar. Sure enough, when I click on the time in the weather/clock widget, nothing happens. When I click on the weather, the weather app opens. My phone is stock running Gingerbread 2.3.3 and not rooted.
I see a weather app in the apps drawer, but there's no clock app. I assume there was one, even though I never accessed it via the apps drawer, always from the clock/weather widget. I do recall seeing a clock app icon in the recently used apps area though. Of course there's no sign of a clock app now.
Initially I just thought the widget broke, so I deleted it and created a new widget. It has the same problem though, and further investigation showed that the entire clock app is gone. I've rebooted the phone multiple times, and I even shut it off overnight hoping the phone had just freaked out temporarily, but the clock app is really gone.
I use the world clock, alarms, timer, stop watch, etc., very frequently, so having them gone is a real pain.
I've read about previous issues with a disappearing people app where a factory reset temporarily fixed the problem only to have the app disappear again shortly thereafter. I'm reticent to do a factory restore, as I've got lots of apps with much config data, and I'd hate to have to recreate all that only to have the same problem.
Help much appreciated!