These 3 genera, in the Crassulaceae family, include plants from many parts of the world.
Astrophytum (Bishop's Hat) is a (mostly) star shaped cactus from north/central Mexico and southern Texas, USA.
The Bromeliads, like Cacti and Agavaceae are a New World family.
Melocactus are recognizable by the large cephalium that develops on mature plants. They are native from Brazil to Southern Mexico, including the Caribbean.
Cissus is one of the largest genera of succulents, and one of the weirdest. Cyphostemma is a member of the Vitaceae or grape family.
Four genera from the subfamily Opuntioideae, all from the Americas.
Euphorbia is one of the largest of the succulent plant families. The genus Euphorbia is found throughout the tropics and semi tropics around the world, with some members of the family growing well into temperate regions.
Parodia, native to the uplands of Argentina, Peru, Bolivia, Brazil, Colombia and Uruguay. Notocactus, with the center of the genus in Brazil and Argentina, but with members throughout the Eastern side of the Andes.
Most of these are from Mexico, although they occur in the southern United States and into South America.
From Mexico and Southern US. Usually having heavy spination and relatively small flowers, the fruits are copiously woolly. Includes the "Golden Barrel Cactus".