Power outages are VERY rare at WDW, however they do happen. Parks are less likely due to above posters notes. I have experienced one myself though, DTD back just before Adventurers Club closed in DTD. My friend and I were in there, most of the lights went out except for the ones on emergency power. The Mask Room was totally dark. We had our drinks and figured we'd hang out and wait for the power to come back on. 20 minutes later, they made an annoucement that the 'Wildebeasts were loose in the club and we would need to evacuate the premises' (I know, but it's the Adventurers Club, they do everything in character).
Outside it was pretty dark and there were Disney supervisors everywhere with the red flashing batons, directing people to the exits and parking lots. Disney police at the traffic lights (also not working) directing traffic away from the DTD area. Later found out most of the area around DTD was without power for several hours that night.
So yes, there is the rare occasion parts of WDW can lose power and the Disney management is well prepared to handle these types of situations.
Sad footnote to this story, this was our last visit to the Adventurer's Club, we had no time to go back and it closed except for private events not long after that.
Kungaloosh!