IMO Octopi belong in the ocean. They require PRISTINE water conditions and most of us cannot provide that environment. As was previously mentioned, they do not live long in captivity so I think that we shouldn't keep them.
I do want to relay a funny story (as best I remember it) I heard about octupi----
There were some marine biologists who were studying octopi and they had one in a big tank in their lab. They were trying to study courtship, hunting habits, etc.
They were also studying some marine fish and had a tank set up in the same lab. A couple times per week, a fish would go missing. No bodies...no skeletons...no increase in Ammonia or Nitrates. Just gone.
They hid a video camera to find out who was stealing their fish. It could have been a guard, the maintenance crew, etc. They were very surprised when they viewed the tape in the morning. The Octopus saw the fish across the room, climbed out of his tank....ran across the floor...grabbed a fish....ran back to it's tank and ate it. By the time people came in the next day, the water had dried on the floor and/or the maintenance crew mopped it up (I don't recall which).
I don't know if this story is true as not everything you read on the internet is true. However, I thought it was funny so I thought I would share.