Octopuses and octopi are both legitimate terms. As a marine biologist friend explained it, octopuses refers to multiple animals of the same species (i.e. red octopuses or giant pacific octopuses). Octopi refers to multiple animals of different species. Take it FWIW ...
Back to the original topic ... there's appropriate and inappropriate ways to interact with marine critters. As several have mentioned, handling an octopus can be fun if you know when to and when not to. They're pretty intelligent critters, and will let you know when it's time to leave them alone (they start changing colors ... and white is their "leave me alone" color). I recently had an encounter with a GPO in Barkley Sound where we had a mid-size octopus (perhaps 4-5 foot tip-to-tip) stretched out like a trampoline. The animal stayed a nice healthy reddish color throughout the encounter, and kept reaching out as more divers (there were six of us present) took off their gloves and offered a hand for a "taste". At one point it had all eight tentacles off the ground and wrapped around a diver's arm. Not once did it change color or try to escape ... it seemed to be enjoying the interaction. Most times, however, octopus will not be so accommodating. If they try to flee, or start turning into living kaleidoscopes, leave 'em alone ... you're just stressing 'em out.
Other critters that are fun to interact with are wolf eels and harbor seals. In both cases you'll need to keep your fingers out of reach of their mouth, as they can give you a nasty bite ... even if they're not intending to harm you. Many wolf eels have the personality of your average golden retriever ... and act accordingly. If you have an urchin handy they'll be your best friend. I had one actually wrap it's body around my leg and stare at me waiting for something to eat. A dive buddy once had a curious harbor seal put it's flippers on either side of her head and stare into her mask. She said she was a bit nervous, but the seal seemed more playful than threatening, and afterward she thought it was a really cool experience.
But I agree that divers should not touch surfaces covered in anemones or other sessile marine life as it damages or kills it.
... Bob (Grateful Diver)