No, California is not going to fall into the ocean. California is firmly planted on the top of the earth’s crust in a location where it spans two tectonic plates. The San Andreas Fault System, which crosses California from the Salton Sea in the south to Cape Mendocino in the north, is the boundary between the Pacific Plate (that includes the Pacific Ocean) and North American Plate (that includes North America). These two plates are moving horizontally (rather than vertically), slowly sliding past one another. The Pacific Plate is moving northwest with respect to the North American Plate at approximately 46 millimeters [or 1.81 inches] per year (the rate that your fingernails grow). The strike-slip earthquakes on the San Andreas Fault are a result of this plate motion. So, although there is nowhere for California to fall, Los Angeles and San Francisco are moving towards one another and will one day be adjacent (see below).
Source: U.S. Geological Service
Also see "Can a Volcanic Eruption Occur in Los Angeles?"
and "Do Tornadoes Occur in Los Angeles County?"