Yakaholic, the Florida DMV states in response to a FAQ:
If the non-motor powered vessel is less than 16 feet in length, it is not required to be registered or titled. However, if the vessel is 16 feet or more in length, it is required to be titled.
I believe if it is titled, it must have registration numbers. Again, no one I know has titled/registered a sea kayak.
Unfortunately, as more restrictions are placed on powerboaters because of their damaging and endangering the marine environment, the powerboaters are prone to blame kayakers/canoeists. Then, the powerboaters complain that if they are being restricted, kayakers/canoeists must also be restricted. Go figure.