Aquaculture means farming aquatic plants or animals. For example, you can raise trout, catfish, oysters, clams, fish for bait, crawfish, or tilapia. You can raise aquatic plants and animals in ponds or in seawater depending on what waters you have access to—for example, oysters are raised in salt water while trout can be raised in a freshwater pond.
Specialty vegetables can mean anything from heirloom varieties of typical farm-grown vegetables and using greenhouses or hydroponics to grow out-of-season crops to farming edible mushrooms such as shiitakes or button mushrooms (agaricus).
Growing feed and forage for livestock is another specialty area. Consider growing plants for birdseed, too: sunflower, millet, and canary grass are popular. You could grow turnips and rutabagas for livestock to forage. If you have the right pasture, you can grow hay for other farmers.
Edible oils like flaxseed and borage, castor beans, and sesame can be good alternative choices. Also consider other popular cooking and cosmetic oils like sunflower, comfrey, jojoba, lupine, milkweed, and safflower.
Fruits and nuts are other kinds of specialty crops. Heirloom apples, Asian pears, berries of all kinds—gooseberries, elderberries, blueberries, strawberries, cranberries and currants—as well as rhubarb, grapes for eating or for making wine, and more, are some good choices. And, if you have maple trees, tapping those trees for maple syrup is another possibility.
Do you have a green thumb? Do you have a nice plot of arable land for growing plants? You can grow vegetable starts and sell flats of them in the spring. Or consider transforming your farm into a nursery. Sell trees, bedding plants, perennials, annuals, bulbs, and more. You can also sell field-grown cut flowers to florists and garden shops for arrangements or drying.
Agroforestry means, basically, farming trees. Christmas tree farms, bamboo, firewood, tree seed collections, and wild nuts are some viable options.
Specialty livestock are those animals that are not commonly farmed. Potential specialty livestock can include beefalo (bison cow hybrid), buffalo, deer, elk (for meat and antlers), pheasant, alpacas and llamas, goats, horses (draft horses, miniatures, exotics), mink, mules and donkeys, rabbits for meat, Angora rabbits for hair, and worms for composting. In terms of specialty poultry items, you can produce balut (partially-incubated duck eggs), partially developed chicken eggs (for Asian markets), ducks for meat and pate, doves, geese, guinea fowl, peafowl and peacocks, pigeons, turkey, and quail.
There are other value-added products you can make on your farm that come as a result of your agricultural endeavors. For example, if you keep bees, in addition to honey, you can sell beeswax products like candles or propolis (bee glue). You can develop a line of herbal tinctures, teas, and salve products made from wildcrafted or farm-grown herbs. As a farm byproduct, you may be able to make specialty products like kombucha, sweet and hard cider, beer, wine, cheese, tanning hides, dried fruits, furniture, wool for spinning or spun into yarn and dyed, processed meat like jerky, salsa, soap—the possibilities are nearly endless.