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
Due to the two inch slippage of the San Andreas fault every year, Los Angeles City Hall is now more than 15 feet closer to San Francisco than when it was built in 1926. Scientists project that it should be located in the suburbs of San Francisco in approximately 15 million years.