The Raspberry Pi is a great little computer to use for a home surveillance system, but most of the projects we've seen have been a bit more advanced. Bitreactive put together a guide for a simple Raspberry Pi alarm that detects motion and sends you an SMS if something happens.
The build here uses a Raspberry Pi, a USB camera and a cheap accelerometer. Every time the system detects a vibration, it snaps a picture, checks to see if there's a change in the image, then sends you an SMS with a picture of the intruder. You probably wouldn't want to use this to protect your bag of jewels, but it's certainly handy for keeping an eye on a pesky cat or roommate.
Intruder detection with Raspberry-Pi [bitreactive]