You can own one. There are many species that come up for sale at pet stores. Do not get a blue ring octopus as they are deadly poisonous (they are still sold frequently, suprisingly). Octopus are very special care pets, and can escape from just about any aquarium. All the octupus I have ever seen for sale have actually been kept in their own cage inside the main tank, just to illustrate how difficult it is to contain them. They have only one bone in their body, their beak, and they can sqeeze through anything that is larger in diameter than their beak. Also, they have amazing prying power and can escape that way as well. They have short life spans, for the most part, as well. Anyway, simple answer to your question is, yes, you can own one. But, do a lot of research and planning before you dive in and buy one.
Kris