The AT24C02 is from Atmel's line of serial EEPROM chips with a whopping capacity of 2K! (256 x 8) That's not a whole lot more than the onboard EEPROM in an Arduino, but it does have the advantage of being external:
it can stay in-situ even if the microcontroller disappears/gets exchanged
multiple devices can share access
There are a few libraries available that encapsulate the interaction with external EEPROMs, but first step is a simple test of the basic read and write capability using the basic Wire library. Surprise, it just works (as long as you get your bits and bytes ordered correctly).