Grimpoteuthis, the Dumbo Octopus. Isn't he cute?
They swim, like Dumbo, by flapping their ears. Or whatever those things are.
Or whatever it was Dumbo did. (I saw the movie when I was four. I realize it was seminal but I'm not that sure on the plot.)
Update 12/2013: A new picture of an even cuter Dumbo Octopus here.
Update 5/2014: A rather more frightening look at a Dumbo Octopus here.
Update 9/2014 a lovely video here.
A new sighting here.
Update Oct 12 2014: A new video here.