depends on the time of year, and slightly what part of fl you are in. Some parts do get frost....
all year: Dinosaur kale (I've had the same dino kale plant growing for about 4 years now), thai basil, regular basil, rosemary, mint, mustard (tastes better in winter), collards (taste better in winter), everglades cherry tomato (if you can find them, they're great and literally can grow in sand, lots of tiny micro tomatoes all year long), okra, pigeon peas, purslane (often seen as a weed, but high in omega fatty acids and very succulent), callaloo, ground peanuts, moringa, katook, peppers
winter: i tend to have better luck with the smaller cherry and pear tomatoes, they're higher yield and take less time to ripen, i.e. less time for pests to get to them, lettuces, beans/peas, arugula, chard, other kales, (watermelon, scallop squash, seminole pumpkin, zucchini, yellow squash- all can be grown, but are highly susceptible to pests and diseases), cilantro, parsley, japanese eggplant do better than italian, chives, broccoli/cauliflower (variegated is fun)
depending on space and what part of florida you're in, you can also grow a huge variety of fruit trees. I personally have: sugar apple, pomegranate, passion fruit (vine), orange, key lime, kaffir lime (great for cooking with leaves, not so much the lime besides lime rind), mangos, starfruit, papaya, jackfruit, everbearing mulberry, guava, jaboticaba
here's a more extensive list:
http://www.tropicalfruitnursery.com/plant-catalog
this is what comes to mind and stuff i've grown. can grow nearly all varieties of peppers, some like manzanos are a little more challenging, but i've seen some success