The term "banana spider" actually refers to three different types of spiders; the Brazilian wandering spider which is poisonous, the golden silk orb-weaver which is not poisonous, and the Argiope appensa which is also not poisonous. While caution is advisable around any spider, knowing the precise arachnid with which you are dealing is vital for safety.
The Brazilian wandering spider is indigenous to the tropical regions of South America, although one species also appears in Central America. All of these are part of the Ctenidae family, all wandering spiders. In the 2010 Guinness Book of World Records, the Brazilian wandering spider is listed as the world's most venomous. The good news is that effective antivenoms are available, but it is still best to avoid bites.
The golden silk orb-weaver appears in many different habitats around the world. In North America, they are often called writing spiders because of the patterns in their webs. Their legs feature stripes with tips pointing inward, a specialization for sewing. Their alternation between green or yellow with black or dark brown signals predators that they have venom, although they actually are not poisonous.
The Argiope appensa is a gold and black spider that is indigenous to islands in the Western Pacific Ocean, although it has also been introduced to New Guinea, Taiwan and Hawaii. The striking alternation of black and gold is the most noticeable feature.