Another random example of what can be done quite easily with an Arduino-based system is a security access system. A popular method is using a numeric keypad, and this is how Instructables user "camilo.n1012" has created theirs. The goal of the system is to activate a device upon entry of the correct PIN using the keypad, and in this example a servo is controlled. You could always replace this with a door strike controlled by a MOSFET, or other devices controlled by relays. Here's an example of the system:
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Although the process described above may be simple for one relay or device, or if you have plenty of time - it can be done reasonably easily. However if you have two or more relays - 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: