From a post on boingboing.net, Merriam Webster editor Kory Stamper discusses the "correct" plural of octopus:
Octopus:octopi is a standard example illustrating ("false") analogy that I've used in class before. The story I've told goes like this: Octopus sounds like a Latin word, and so by analogy to Latin borrowings like syllabus:syllabi, alumnus:alumni, people often form its plural as octopi. But, so the standard story goes, it's not a borrowing from Latin, but rather from Greek, so octopi is technically incorrect. The proper Greek plural is rather octopodes.
[More technically, it is a borrowing from Latin, but the Latin word itself is a borrowing/coinage from Greek, and the Greek word would be (in nominative singular) ὀκτώπους (oktṓpous), whose (nominative) plural would be ὀκτώποδες (oktṓpodes). Given that it's a scientific name, it will in fact be a Latin word (albeit one of Greek origins). By modern Latin rules for Greek borrowings, it should be a third declension noun, and form its plural with -es. Thus the Latin forms are octopus:octopodes.]
In the video, however, Stamper makes the following arguments: (1) octopodes sounds rather pedantic (I think a good compromise here though is to pronounce it to rhyme with nodes), and (2) once a word is borrowed into English, it becomes an English word and so should form its plural according to the standard English rules for pluralisation, i.e. it should be octopuses.
In fact, though it is true that -s is the dominant plural ending in English, and thus the one usually used for borrowings and new coinages, it is not the only possibility. Even coinages don't always form plural with -s. For example, there is a powerful text-editing program called Emacs. Different varieties of this program have arisen, and thus a plural form is sometimes called for. And the standard plural used is Emacsen (by analogy to ox:oxen; cf. boxen and VAXen). The point being simply that if even coinages don't always use the -s plural, then we needn't expect that borrowings should either. And therefore, nothing forces us to accept octopuses as the "correct" plural. [Caveat: of course there is no real "correct" plural for any word, aside from whatever people accept/use.]
But, as it stands, it would seem that the "correct" pluralshould be either octopuses, since that conforms to the dominant pluralisation rule for English, or else octopodes, since octopus is a coinage made from Greek components.
As one of the commenters to the boingboing post (Anon #80) points out though, there is in fact a case to be made for octopi as the "historically correct plural". The case is as follows: Linnaeus may have coined octopus ("eight foot (creature)") by analogy to the old Latin word for "octopus", namely polypus ("many foot (creature)"). Now polypus is obviously also a borrowing from Greek, but in Latin the normal plural of polypus was in fact polypi! (And, likewise, the plural of the modern scientific term polypus is also polypi).
[The commenter goes on to add that even the Greeks sometimes treated πολύπους (polúpous) as a second declension noun (which would give it a nominative plural of πολύποι (polúpoi). So even the Romans might have had a precedent for their -i plural of polypus.]
So if octopus is seen as a modern "updating" of the original Latin word for "octopus" (polypus), then there is an interesting case to be made for octopi as the (historically) "correct" plural.