Why do thunderstorms knock out power?
Considering the number of lightning strikes on or near power lines, power going out as a result of one is actually quite rare.  Overhead power lines do have cables that run above them mostly for the purpose of catching lightning strikes.  These cable are then periodically grounded at poles.

Lightning is a massive current surge, and sometimes stuff happens.  It's not economical to protect against every last lightning scenario, so the systems are designed to keep on going with most lightning strikes.  However, just the right strike at just the right place at the right time can still cause excessive current someplace, which trips a breaker, which shuts down power for a while.  Breakers on intermediate distribution lines usually reset themselves after a few seconds a few times in a row.  This is why you are more likely to see power blip out for a few seconds after a lightning strike than a real outage a crew has to come out and fix, which will take 10s of minutes to hours.

Actual outages due to lightning are actually more likely due to lightning making a tree branch fall accross a intermediate feeder line, which then shorts the line and causes a breaker to trip.  The big cross country high voltage transmission lines are quite well protected against lightning, and you very rarely hear of a outage caused by a strike to them.  Usually lightning outages are geographically small since it is the intermediate feeders (a few kV to a few 10s of kV) that are effected by tree branches and the like.