It is known that algebraic spaces are fpqc sheaves. A proof by Gabber can be found in the Stacks Project at tag 0APL.
Naturally one may ask whether this generalizes to algebraic stacks. Given an algebraic stack $\mathcal X$, is it true in general that $\mathcal X$ is a stack in the fpqc topology?
Remark. Following the proof of Gabber one can show that if there exists a smooth ind-quasi-affine surjection from a disjoint union of affine schemes then the answer is true. However this seems to indicate that the answer may be false in general.