A morphism of varieties over $\mathbb{C}$, $f:V\to W$ is proper if it is universally closed and separated. One way to check properness is the valuative criterion.

What other methods do we have for determining if a morphism is proper? Particularly, I'm interested in quasi-projective varieties, but ones that aren't actually projective. And while a completely algebraic, valid over all fields or for schemes answer would also be good, I'm looking at complex varieties, and may be able to assume that the singularities are all finite quotient singularities.