What Arduino model? - Not all models have built in EEPROM memory that will preserve data across power off.
How much data? - The UNO only has 1K (1024 bytes) of EEPROM memory available and other models may have more/less.
How often will it be changed? EEPROM memory is only good for about 100,000 times writing (lots more reading) so if the data changes much the memory will not last long before you get write errors.
You could also use an SD memory card with suitable adaptor.
Somewhere on here I have seen someone testing a new bootloader that allows the flash memory to be altered during normal program execution (usually this can only happen during bootloading) so you might be able to find/use that.