Experimenting with remote controls is funa and can lead to creating useful projects, and one of these is by Instructables member bergerab who demonstrates how to control an Arduino via infra-red remote control and thus a mains power outlet. Although they only work over a line-of-sight distance, IR remotes are very easy to use and can send many commands without much effort.
Thanks to Ken Shirriff's excellent Arduino library you can also work with these handy remotes, and even use the remote from your TV or other household appliance with your Arduino. The tutorial details how to control mains current via a relay, which we don't recommend you do unless you're a licensed electrician. However the theory is applicable to other projects and thus worth studying.