I have encountered the opinion that the correct plurals of octopus and platypus are octopodes and platypodes, because that's how they are pluralized in Greek. This argument might make sense if a) the words were borrowed from Greek, or b) these plural forms were found in English usage.
But neither is true. The words are borrowed from scientific Latin octopus and Platypus, which in turn are borrowed from Greek. Merriam-Webster's Dictionary of English Usage notes that octopodes is never found in context; it's only used in discussions, like this one, about whether it is the correct plural form. (But I did find one in-context occurrence.) The same situation seems to hold with platypodes. The OED lists octopodes and platypodes as plural forms, but provides no actual citations with these forms. Judging from the citations, the most common plurals are octopuses and platypuses, closely followed by octopi and platypi.
I don't know if the scientific Latin words even have plural forms. If they had plurals, I'm pretty sure they wouldn't be formed with -podes. And since they are borrowed from Greek, they are not second declension -us nouns and would not be pluralized octopi and platypi. But octopi and platypi, altho they are unetymological, are in use in English, and usage trumps etymology every time.
It's also interesting to note that the Greek words don't mean what the English words mean: ὀκτώπους (oktōpous) means "eight feet long", and πλατύπους (platupous) means "flat-footed".
Update! It seems that Greek third declension nouns are borrowed as Latin third declension nouns with the stem change mimicking the stem change in Greek, so the Latin plural of "octopus" would indeed be "octopodes".