Heard of these? They're little C-programmable boards with a bunch of I/O things on them where you can hook stuff up. For instance, you could hook up the anode on an LED to port 7 (Or whatever number you want), then hook the short leg to the ground, then code it so that it sends enough power through port 7 to turn on the LED, and then the LED turns on when the Arduino is receiving power. You can program it to blink every 2 seconds, or whatever you want.

I'm going to get an LCD screen and some buttons and a speaker and make a game for it.

So far I've just hooked it up to my seven-segment display and made it count from 1-9, then reset back to 1 and do it again. They've got tons of coding tutorials on their website. Definitely worth buying.

A bit late posting here but, it's nice to see you found Arduino.  You can build a lot of different things with that micro-controller and you are helping the open source community keep us posted on your projects, I'd like to see some pics/videos if you get anything cool going.