I had an alligator chase me off a water hole on a course in Ft Meyers. They can move fast in short bursts, dam thing came out of the water fast! Anyway, we chased it down and ran over it with our golf cart.
Seriously though.. You wouldn't want to swim in any body of water they populate. Muddy, swampy, stagnant stinky stuff.. Normally.
I've been to Florida at least 10 times, to both the east and west coast. I've been fishing in rivers and swamps by boat a few, in perfect alligator habitat and I've yet to see one.