Squirrels contributed to two power outages in Portland, OR in one week, and PG&E crews there are considering "wildlife guards" to prevent squirrels from entering substations, since 18% of power outages there can be blamed on animals. One of these power outages was blamed for two car accidents. Squirrels were also later falsely accused of a power outage in nearby Clackamas County, but it turned out to be an equipment failure.
In Nebraska City, a squirrel "put his feet where they shouldn't have been," leaving residents without power for an hour. One squirrel caused inconveniences for over 4000 people in Indiana, and a squirrel in Springfield, IL made contact with the power equipment "in the wrong way" (I think that is a euphemism for the squirrel's passing). Grand Rapids, MI also experienced a squirrel-related loss of power.
And finally, in Leatherland (somewhere in the UK), a squirrel started a fire after he "fried his brains out," and the short circuit triggered a fire in leaves nearby.
In case you are wondering, it's not squirrels' running on single power lines that causes the problems; it's almost always contact with two lines at the same time (even a paw on one, and a touch of the tail to the other) that causes the outages. A nice description of the problem here.