If I made a list of words I often see misspelt, definitely would definitely be among them. But while it was once *definately or *definatly I’d read in casual, unedited writing, nowadays it’s more likely to be defiantly. I ran a search on Twitter:
The figure is taken from thin air, but it might not be far wrong: see for yourself. Defiantly is used a couple of times a minute around the world on Twitter, almost always to mean definitely. I suspect that’s also the case in text and instant messaging, but I haven’t looked into it.
In fact, just about the only time we see defiantly ≠ definitely on Twitter, it’s not because someone is using defiantly to mean defiantly, but because they’re mentioning it to complain about the misspelling.
It could be, as @GramrgednAngel suggested, that people are typing definat… (like in the good ol’ days) and autocorrect is transposing this into defiantly. If so, it’s having a big influence.
I’ve not heard the error in speech, nor yet spotted it in print; for now it seems mainly restricted to informal digital communication. But who’s to say it won’t spread, defiantly.