[gh02t]

Every ESP8266 module I've ever used had a chunk of flash memory you could use for persistent storage that survived reboots/poweroff too. It's used to store WiFi credentials in a lot of frameworks, but you can stick other data in there. I guess it's not integrated into the chip, but don't most people use the integrated modules even in custom designs? All mine have.

Also IIRC it's not as well known, but the RTC also has a very tiny amount of memory you can use to pass state between deep sleep cycles. That one won't survive a power loss, but it's handy when sleeping and doesn't wear out like the flash memory.