There are many (thousands) of species, but generally, one can group them into ball-like (globose); columnar (standing like a column) and those with segments, like prickly pears - members of the cactus family are highly diverse and live in many climates.
There are nearly 2000 different varieties of cactus plants. Columnar cacti, ocotillo, cholla, pincushion cacti, totem pole, barrel cactus, fishhook are some of them.
The most familiar is the prickly pear. There is also the hedgehog and pincushion plant. There is also the totem pole which is quite majestic and known for its height.