Bostrom & Ćirković (pages 1 and 2):
The term 'global catastrophic risk' lacks a sharp definition. We use it to refer, loosely, to a risk that might have the potential to inflict serious damage to human well-being on a global scale.
[...] a catastrophe that caused 10,000 fatalities or 10 billion dollars worth of economic damage (e.g., a major earthquake) would not qualify as a global catastrophe. A catastrophe that caused 10 million fatalities or 10 trillion dollars worth of economic loss (e.g., an influenza pandemic) would count as a global catastrophe, even if some region of the world escaped unscathed. As for disasters falling between these points, the definition is vague. The stipulation of a precise cut-off does not appear needful at this stage. [emphasis added]
Open Philanthropy Project/GiveWell:
risks that could be bad enough to change the very long-term trajectory of humanity in a less favorable direction (e.g. ranging from a dramatic slowdown in the improvement of global standards of living to the end of industrial civilization or human extinction).
Global Challenges Foundation:
threats that can eliminate at least 10% of the global population.
Wikipedia (drawing on Bostrom's works):
a hypothetical future event which could damage human well-being on a global scale, even endangering or destroying modern civilization. [...]
any risk that is at least "global" in scope, and is not subjectively "imperceptible" in intensity.
Yassif (appearing to be writing for the Open Philanthropy Project):
By our working definition, a GCR is something that could permanently alter the trajectory of human civilization in a way that would undermine its long-term potential or, in the most extreme case, threaten its survival. This prompts the question: How severe would a pandemic need to be to create such a catastrophic outcome? [This is followed by interesting discussion of that question.]
Beckstead (writing for Open Philanthropy Project/GiveWell):
the Open Philanthropy Project’s work on global catastrophic risks focuses on both potential outright extinction events and global catastrophes that, while not threatening direct extinction, could have deaths amounting to a significant fraction of the world’s population or cause global disruptions far outside the range of historical experience.
[Note that Beckstead might not be saying that global catastrophes are defined as those that "could have deaths amounting to a significant fraction of the world’s population or cause global disruptions far outside the range of historical experience". He might instead mean that OPP is focused on the relatively extreme subset of global catastrophes which fit that description. It may be worth noting that he later quotes OPP's other, earlier definition of GCRs, which I listed above.]
I intend to add to this list over time. If you know of other relevant work, please mention it in a comment.
My impression is that, at least in EA-type circles, the term "global catastrophic risk" is typically used for events substantially larger than things which cause "10 million fatalities or 10 trillion dollars worth of economic loss (e.g., an influenza pandemic)".
E.g., the Global Challenges Foundation's definition implies that the catastrophe would have to be able to eliminate at least ~750 million people, which is 75 times higher than the number Bostrom & Ćirković give. And I'm aware of at least some x-risk focused EAs whose impression is that the rough cutoff would be 100 million fatalities.
With that in mind, I also find it interesting to note that Bostrom & Ćirković gave the "10 million fatalities" figure as indicating something clearly is a GCR, rather than as the lower threshold that a risk must clear in order to be a GCR. From their loose definition, it seems entirely plausible that, for example, a risk with 1 million fatalities might be a GCR.
That said, I do agree that "The stipulation of a precise cut-off does not appear needful at this stage." Personally, I plan to continue to use the term in a quite loose way, but probably primarily for risks that could cause much more than 10 million fatalities.
There is now a Stanford Existential Risk Initiative, which (confusingly) describes itself as:
a collaboration between Stanford faculty and students dedicated to mitigating global catastrophic risks (GCRs). Our goal is to foster engagement from students and professors to produce meaningful work aiming to preserve the future of humanity by providing skill, knowledge development, networking, and professional pathways for Stanford community members interested in pursuing GCR reduction.
And they write:
What is a Global Catastrophic Risk?
We think of globa