I've had my browser home page set to http://onlineclock.net. It's a huge clock in the old school LED style. Looks just like the alarm clock sitting next to my bed at home. You can even set an alarm. It's all done in javascript, so it will still run when you disconnect from the network...although it does send you to an "alarm" page when it goes off, so you'll need it to be online to get the alarm sound/message. I think it would be easy to develop something similar to run locally via a file:// URL. I might have to try that.

Incidentally, there's also a stopwatch (http://stopwatch.onlineclock.net).