As long as the power outage is under 12 hours long then you generally will not experience anything disasterous, depending on the species of livestock in your tank.
If you are truely worried, you can go to any computer hardware store and buy a backup UPS power source that will keep the tank running anywhere from 2 - 24 hours depending on the size of your tank and the model of UPS you buy. They are not cheap though, but I'm sure you are used to that with this hobby.
If the power outage is short, you can get away with blowing into a air tube with an airstone on the end from time to time and gently stirring the water with a spatula.
ps- your critters may do really weird things during a power outage such as anemones turning inside-out and whatnot, but they will recover perfectly as long as the outage isn't over 12 hours.