I was always under the impression that a Lightning rod worked to protect a building by being the tallest part of the building and having a low path of resistance to the ground, thus being a good target for lightning to hit, reducing the chances of lightning strikes elsewhere on the building.
However when reading an Ars technica article, one comment (from user "malor") said that theory is incorrect, and explained that a lightning rod actually prevents lightning strikes in the first place:
Lightning happens when a really huge negative charge builds up in the ground, corresponding to a positive charge overhead, and the differential becomes sufficient to jump the gap. (and, as others are pointing out repeatedly, air is an excellent insulator, so it takes a whacking huge voltage differential to make the arc.)
A lightning rod doesn't exist to provide a spot for the lightning to strike. Rather, it exists to dissipate the charge so that the strike never happens at all. This comes from early experiments with the Leyden jar; if a pointed metal rod was attached to the jar, it wouldn't charge. The electrons are able to leap off a pointed tip, and into the air, dissipating charge as fast as it accumulates. The lightning rod does the same thing, on a larger scale; it spits out electrons into the air like crazy, so that the charge won't build up sufficiently, and the lightning never hits at all.
Now, if the charge accumulates faster than the rod can dissipate it, there can still be a lightning strike, and the rod typically IS the best route to ground. But everything around the rod is going to take a hell of a jolt anyway, including, most likely, your electronics. A lightning rod getting hit means it failed to work adequately; ideally, it should never be hit at all.
How does a lightning rod actually work? Does a lightning rod actually prevent lightning strikes?