It's fairly complex as far as Arduino Projects go (it involves timer interrupts, a Serial Peripheral Interface with shift registers, and a homemade PCB), but hey, I managed to do it, and I didn't have a lot of prior experience with either C or hobby electronics.
http://diydrones.com/profiles/blogs/aeroquadan-arduinopowere...
The official Arduino blog always has lots of interesting examples too - http://arduino.cc/blog/
http://www.janspace.com/b2evolution/arduino.php/2010/06/26/s...
There's also some interesting stuff if you poke around hackaday.com
If you're interested in learning the whole parts procurement process, you can also buy a PCB of pretty much any arduino-based board with no components, then pick out the components you want yourself and solder away.
You can desolder and reuse pretty much any component: connectors, passive elements (resistors, capacitors), switches, active elements (diodes, transistors), LEDs, speakers, relays. You can even reuse bigger functional blocks like power supplies or power amplifiers. I used to do this all the time when I was a teenager.
Nothing like having an idea at midnight and scavenging the components to try it out at once, and not having to wait next day to buy them. Plus, it reduces e-waste, which is horrible to recycle, despite what we are told.
And stay safe, learn you electric safety rules!
PS: nice first project idea - light alarm that wakes you up in the morning, like the fancy, pretty expensive Phillips Wake-up Light Alarm devices. Later, make the light able to fade-in using maybe a thyristor. A nice enclosure is hard to make though - that's where Phillips has the advantage.
Can anyone give examples of the more interesting projects that are being done with the Arduino that you know of?