There's many methods of remotely-controlling an Arduino over the Internet, (such as teleduino) and another method has been demonstrated by Instructables user "geo bruce". In this version a Linux server running PHP connected to an Arduino is remotely controlled via a simple user-created webpage. In this example a light is controlled via a relay, however you can of course control other things. The control is by simple serial commands from the server to the Arduono, which acts on the incoming characters. For example:
If you're looking for a simple way to control many relays from your Arduino, without using up all your digital I/O pins - check out our Relay8: driver shield:
So what is the RELAY8:? It's a new Arduino shield that allows you to drive up to 8 relays from your Arduino using just 2 I/O pins with this shield. It communicates with your board using I2C, so you can even stack several shields together to drive 16, 24, or more outputs! Includes back-EMF protection and works with a wide range of relays. Perfect for home automation projects! For more information and to order, click here.