My aunt was an archaeologist in the Yucatan, and these naturally occurring sinkholes are all over the place. They're called cenotes. The ancient inhabitants used to throw maidens into them as sacrifices.
There have been several articles in National Geographic from the 1960s forward. A recent one showed photographs of a cenote that's connected with the ocean by underground passages. Some (really brave and really stupid) scuba divers actually went through.
Yeah Florida's aquifer runs underground all over the state, we're full of underwater caverns and sinkholes. Way back when I was at FSU we had professors that had mapped miles (held a world record IIRC) of underground caverns connecting lakes all over the place. I actually got college credits learning to scuba dive.
When I was a kid, I remember folks studying the lakes around town dropping bright dye in one, only to have it pop up in other lakes a ways off.