There is a saying that necessity is the mother of invention. This holds true in fishing as well, as a result, there are many odd ways of fishing. Most of these methods have been dreamed up for people who are fishing for food, or who enjoy fishing games.
It is important when you decide to try an odd way of fishing that you check the local fishing regulations first. Game wardens are not impressed with creativity.
In the south, jug fishing is popular. Tie a ten foot line with a weight and hook, onto an empty gallon milk jug. This makes a good fishing rig. If you paddle out in a canoe or flat bottom boat you can fish with 20 or so jugs all thrown out around the boat.
When a fish takes the bait the jug will start to move away. All you have to do is chase it with the boat and grab the handle of the jug. To real it in, hold the handle and wrap the line around the jug. Jug fishing at night is a fun pastime. If fishing is slow you can always play online fishing games.
Another odd way of fishing is fishing by hand. Catfish noodling is another example of such fishing.
Fishing for Buffalo fish by hand is quite the challenge. It is doable mainly in shallow rivers by standing in the water with your feet spread apart, bent over, and your hands in the water between your legs. Along the bottom of the river, pour a can of corn between your legs. When the fish come to eat, grab them by the gills.
Another odd way to fish is with a bow and arrow. You can mount a fishing reel on the front of the bow. Next tie the line to the back of the arrow. You can fish in shallow lakes and river for Catfish, Carp, and Buffalo fish. When you see one you shoot it with the arrow and then reel it in.