

Florida has had earthquakes, but they are rather infrequent and are not known to be severe. A 6.0 magnitude earthquake occurred about 260 miles off of Florida's west coast in September, 2006. Fortunately, there were no injuries or fatalities. Compared to California and the west coast of the U.S., the seismic hazards in the East are not well-understood. So, it is obviously possible for Florida to have a damaging earthquake, but it's pretty unlikely. In the last 200 years, very large earthquakes have occurred in Missouri and South Carolina. The Missouri earthquake was large enough to reroute the Mississippi River and the South Carolina earthquake was felt as far away as New York City and was strongly felt in Florida.

The USGS states that several minor shocks have occurred in Florida, with only one causing damage, St. Augustine January 1879:

Near St. Augustine, St. Johns County, Florida
1879 01 13 04:45 UTC (local Jan 12)
Intensity VI

Plaster was shaken down and articles were thrown from shelves at St. Augustine and, to the south, at Daytona Beach. At Tampa, a trembling motion was preceded by a rumbling sound. Felt from a line joining Tallahassee, Florida, to Savannah, Georgia, on the north to a line joining 
Punta Rasa and Daytona Beach, Florida, on the south. Two shocks occurred, each lasting 30 seconds.

Major earthquakes in the vicinity of Florida have also sent shocks into the state including the Charleston, South Carolina earthquake of 1886.

More information regarding Florida earthquakes can be found at the US Geological Survey

Florida has earthquakes, but they are infrequent and typically not severe.