While not for the electronics newbie, several recent projects detail ways that you can monitor an alarm system – or any similar device – using text messages and wireless connectivity. Here are two of the more interesting ones:
Using the Electric Imp (an great project by itself!): http://www.swblabs.com/?p=801
As off-the-shelf products allow more devices to be connected and controlled via networks, this concept will almost certainly gain popularity for low-security applications.