Factory reset protection is a hot new feature, and one that's catching a lot of people out, judging by how many questions we get about how to get around it.
These questions are all asking pretty much the same thing, but the answer depends strongly on what phone is involved (and will change for different firmware versions too). The situation is somewhat analogous to "how do I root my phone?" or "how do I install a custom ROM?" questions, and like those topics, I think there's a risk of these questions getting messy. Unlike "how do I root my device?" we should expect that the answer for the majority of phones will simply be "you just can't", so I'm not sure if the "one question per phone" approach will work here: we'd end up with a lot of unanswered questions. OTOH, it's likely that if someone discovers a way to bypass it for a phone where it was previously thought impossible, they might ask and self-answer a question about that phone, and I think we want to encourage that (rather than closing the question and making them merge the answer by hand).
Matthew Read's answer is pretty close to being a canonical answer for this question, but the question it's on is for one phone only, and of course the answer only deals with a small selection of phones. I'm not sure that trying to edit this question to be more generic and then making the answer community wiki is the right thing to do here; nor does breaking up the existing good answer into answers on separate per-phone questions.
I'm a bit lost about what we should do, and I think that now is the time to act, before we have a spaghetti dish of overlapping questions to clean up. I'd like to hear the community's opinions on what's the best option, or to hear some new and better options.