I live in the Los Angeles area and we have earthquakes here every once in a while. And the "Big One" is supposedly coming. They have earthquakes in San Francisco too (i.e. the infamous 1906 earthquake). I believe that here in L.A. it is illegal for a house to have a basement (my house doesn't have one, and I haven't been to one that does) because of the earthquakes. So why do these two cities have underground subway systems? Isn't it dangerous?

Basements are not common in L.A., but it is not illegal to have one, so first of all - get your facts straight. The BART system in San Francisco was built to sustain a major earthquake and, in fact, came through just fine in the 6.9 Loma Prieta earthquake of 1989. Some of the worst damage, in fact, was sustained by above-ground infrastructure - like the Bay Bridge, Interstate 880 in Oakland and the Embarcadero Freeway in SF. The bridge was closed for weeks, the Embarcadero Freeway had to be torn down as it couldn't be repaired. So the lesson seems to be that bridges and freeways don't do so well in earthquakes, but subways are fine!