If you have a fireplace with a remote ignition controller, this project may be of interest. On the geek-tips website, they've described how to modify remote-ignition controllers with Ethernet-enabled Arduino boards so they can be easily turned on or off via a connected device. Like most devices with simple button control the modification is simple, and with theteleduino system you could even do this from almost anywhere. However it would be wise to consider the unwanted possibilities of such as system - you don't want any "unrequested" ignitions!
Nevertheless, check out the project page for more information. And for more, we're on twitter and Google+, so follow us for news and product updates as well.
If you're looking for an Ethernet-enabled Arduino-compatible board, consider one of Ethernet-enabled boards, such as the Freetronics EtherTen - the Arduino Uno-compatible with onboard Ethernet, microSD socket and optional PoE:
... or for more program space, I/O ports consider the Freetronics EtherMega - the Arduino Mega2560-compatible with onboard Ethernet, microSD socket and optional PoE: