Lake Kissimmee, which has large gators that will take your breath away: the state park there rents kayaks.
I'm really not trying to sound crusty, but here it goes:
I have lived in Florida all of my life (except for two tours in the Navy). I swam in lakes as a kid, had a classmate get mauled by a gator in college, and currently kayak and boat in waters that hold very large gators. I have been hissed at, growled at, etc.
JD's advice is right on.
I only know of one gator "attack" on a kayak (other than the recent video of the gator going after the dog). http://news.google.com/newspapers?nid=1346&dat=20020204&id=HL8wAAAAIBAJ&sjid=pP0DAAAAIBAJ&pg=6384,4381127 You be the judge.
Paddle-craft are very stealthy and you can unintentionally sneak up or worse, on top of, a submerged/rising gator. When this happens the gator will cause a ruckus (read "water explosion"). I have had this happen next to me while canoe fishing and I know of at least one instance where a kayaker was blown off his boat. This happens more often with the "gentle" manatee. None were attacks, just a freaked out large animal trying to get away.
There has also been the occasional deliberate gator bump to a kayak which is probably a warning shot. I have heard of at least 3 occurences of this.
When folks ask me about kayaking and gators, I always ask, "Do bears keep you from hiking and camping?" No, because your knowledge and respect gives you confidence that you will be safe.
When a gator sees you and submerges, this is passive behavior. However, if he raises his back and tail high, this is a challenge. In response, I turn my kayak parallel to him and show him my 16 feet of orange "what the hell is that???!!" kayak and that usually makes them submerge...if they don't, I find somewhere else to fish. When this happens, I watch to see why the gator wanted me out. It has been due to baby gators in the area that I did not see, I was in his hunting grounds, or I was in his path as he was going from point A to point B.
Hope this helps,
Phil