One of my favorite times of year in my youth was when the rays were running offshore and we'd go out there to catch the cobia that swim underneath the giant mantas:
Boing Boing has a great shot of one flying. It's an incredible feeling to stand on the bow of the boat on the lookout for these enormous-yet-graceful creatures. Even better is casting my rod just right so that it lands under the wingspan where the bait can catch the attention of a cobia (which are delicious).
Forget swimming with dolphins. The next big thing might just be sea turtles. In another "Florida experiences" story, a few years ago my brother and I were hanging out on the beach until just after dusk when we saw something big pop its head above the surface. We stood jaw-dropped as a huge Loggerhead made its way to the beach and up to the dune. That one eventually turned around and went back to sea without laying any eggs. I'm not sure if it was us bothering her or the wind wasn't right, or perhaps it just wasn't dark enough yet. We were amazed enough to go back later that night with flashlights and watch 4 or 5 other turtles go through this time-honored ritual (something like the march of the penguins) where these ladies trek back to the very spot where they were born each year to lay eggs. It's a laborious process that takes about an hour. She crawls to the dune, digs a DEEP hole with her back flippers, lays an average of 100 eggs, cries (forget crocodile tears! there are turtle tears! now with more alliteration!), and then covers the hole and heads back to sea, never to meet her 100 little ones. It's a truly moving experience that I recommend to anyone who happens to be in a "turtle watching" area.