As Etienne said in his answer, you can use the backup registers or backup SRAM but those imply having a backup power source. What I have done for the STM32F3, is use the Flash as an Emulated EEPROM. The drivers are on the ST website, you reserve a few pages of Flash as your 'EEPROM' and write whatever information you want there. On startup your device can read those values or modify them during program execution.
Described here: AN3969.(Application Note from ST, you can just google the ref. #)
A safety measure wold be to change linker file so those flash pages don't accidentally get overwritten if your code should grow larger.