Various species of prickly pear and cholla
Claret cup cactus
Hedgehog cactus
Peyote
Rainbow cactus
Corncob cactus
Living rock cactus
Button cactus
Eagle claw cactus (aka Turk's head cactus)
Fish hook barrel cactus
Pincushion cactus
Strawberry cactus
several others