One result along those lines is that that any algebraic space which has a quasi-finite morphism to a scheme is itself a scheme.
More precisely, if $f:X\to Y$ is a separated, locally quasi-finite, locally finite type morphism from an algebraic space to a scheme, then by the Stein factorization theorem, $f$ is quasi-affine, so $X$ must be a scheme. If you want more details, this is Corollary 17.8 in my notes from Martin Olsson's stacks course.