wildbill:
If you have wifi in your house, it might be easier (though more expensive) to use a wifi shield - then you won't have to run ethernet cable to the garage.You might also consider having the arduino close the door for you - then it can just send a scolding email to let you know it has taken care of the issue.
The Wifi Shields are killers in terms of cost at the moment - a much cheaper and more flexible way is to look at a TP-Link WNR703 router. $25 - You can get a USB/TTL breakout cable from it for $3 from EBAY.
This then acts like a Serial port to the arduino and anything sent out is caught by Linux on TP-link - the TP-Link can be hardwired ethernet or Wireless (or 3G if that floats your boat)
Using Standard linux it can then act to send emails, fire off prowl alerts etc.
Much cheaper than an ethernet shield and/or a wifi shield and much less resources required on the Arduino
Craig