The Arduino platform is ideal for simple interfacing between sensors and external devices, and with a few hours work you can reproduce much more expensive commercial products. One example of this is a thermostat, and Instructables user "Dylon124" has created a simple but effective thermostat that not only has a clean user-interface, but also stores the required setting in EEPROM so power outages won't affect the temperature:
Further along in the project there is mention of controlling mains power via a relay, which technically is an easy thing to do - however a licensed electrician may be required in some jurisdictions. Either way, it's a good demonstration of what is possible - so visit the Instructable for all the details. And for more, we're on twitter and Google+, so follow us for news and product updates as well.
If you have to control one or more relays, and do so neatly with a level of organisation - it's much easier to use dedicated relay control boards. Here at Freetronics we have the RELAY4: board, perfect for controlling up to four relays with Arduino (or any other microcontroller's) digital output pins:
Or if you'd like to control up to eight relays - or more at once with an Arduino Uno or compatible board - consider our RELAY8: board. Controlled via I2C, you can stack up to eight shields with the appropriate power supply to support 64 relays at once: