For me it would take a situation where I was on the verge on panhandling, all other potential resources completely exhausted. When my wife died with no health insurance, no life insurance, and a $120k hospital bill I still wasn't thinking GoFundMe.
But it seems many people are quick to ask, probably because we see so many very generous success stories and hey it's pretty easy to do. I'm referring specifically to someone setting one up for themselves. If someone else does it for you without your knowledge, I think that's far more acceptable. Maybe it's a pride thing.
I've donated to a few, sometimes for someone I knew and sometimes just because their story moved me like the bus lady who was despicably harassed because I remember enduring extreme harassment that can often leads to things like teen suicide.
And then there's the people who set one up to pay for their honeymoon.