It depends what amount of data you want to save. A good and very safe option is using I2C RTC 8253 that has 256 bytes of SRAM also. To modify a byte in SRAM you must follow I2C protocol so some inintentional writes are almost imposible.
If you combine it with power supply monitor and a watchdog timer like DS1232 you get a pretty failsafe system.
I'm using it for a few years, I have installed some systems where I store config data in SRAM and read it at power up. Writing is done when one modifies the parameters. Instead of using lithium battery, you can use gold cap 1F/5.5V. It has enough energy to store data up to 30 days. To achieve maximum read/write speed, you should mannualy tune your I2C routines to get minimum delays in a write signals (4.5 us for a low speed I2C transfer) and therefore you get a theoreticah speed of 10k bytes per second.