For something different, preparing for a future industrial society, a wacky gift or if you're a Seymour Skinner fan - consider making a metric clock. Metric you say? Yes - one day = ten hours, six AM is 2:5:0:000, and so on. Using it might be difficult, but making it won't be using an Arduino and LCD module.
If the metric clock is a little far-out, you can still make a variety of clocks and timepieces based around an Arduino-compatible board. And the most important part of any clock project is the inclusion of an accurate real-time clock IC. Here at Freetronics we have the Maxim DS3232 real-time clock IC module:
Apart from keeping accurate time for years due to the temperature-controlled oscillator and having a tiny coin-cell for backup, it is very simple to connect to your Arduino project. A driver library allows your program to easily set or read the time and date. Perfect for clock projects, dataloggers or anything that needs to know the date and time. Furthermore it contains a digital thermometer and 236 bytes of non-volatile memory to store user settings and other data. For more information, check out the module page here.