I always unplug. A few years ago we had a nasty storm with thunder and lightening. I had my then dial up computer plugged into the phone bit disconnected to the electricity.
Unknown to me we had a lightening strike. It went along the phone cable and burnt out a very new modem. Surge protectors are there for an unexpected surge or spike in electricity, not for lightening strikes.
So, I always unplug everything after I have used it, even the humble kettle - only one exception - the fridge/freezer. That will have to take its chances!