Surge protectors are great for protecting sensitive equipment due to high voltage spikes, such as caused by lightning. Most people do not have a whole house protection system and you will see them add them for computers, TV's' and equipment sensitive to those circumstances. My power strips also have surge protection, but they main reason I have them there is to seperate the equipment that I shut down on a water change and the ones that I do not.
I am not aware of any filters that require recommend them, but that doesn't mean you shouldn't follow the manufacturers recommendations.
My AquaClear 110 (500, HOB power filter) has been through many a power outtage (and I mean many). It started up perfectly everytime with no problems at all. The only reason it might not start up properly is if the water level gets too low in the tank, it's not strong enough to suck the water up very far after it's stopped. And as above keep the impeller area clean.