There are many words in English -- usually words that end in "-us" that people will often pluralize (sometimes incorrectly) with the Latin style "-i" rather than making it an irregular plural of simply adding an "s". When did this become a popular trend?
I don't know if has ever become "common." There are very few words like this and I'm not sure they have consistent handling.
Google Ngrams is great for this kind of "when did people say X instead of Y?" question, even with all of its methodological issues (bad OCR, bad metadata, etc.).
Here are a few queries I ran:
octopuses/octopi: octopi more common before 1921, then octopuses dominant (but not exclusive).
viruses/virii: virii barely registers, ever. Effectively zero, and the hits there are seem to be OCR errors.
platypuses/platypi: has the hallmarks of a small sample size (big, blocky jumps), seems like platypuses mostly dominant but a small showing for platypi.
cactuses/cacti: cacti dominant, but cactuses still there.
I couldn't think of any other words like this off the top of my head. From the above, I don't see any major trends.
A trend that happens with latinized plurals in English is that some of the words, like octopus and platypus, actually come from Greek. Octopus in the plural is octopodes if trying to correctly make it plural by its root language. Both plurals for these words commonly used in English are "correct" though.