In algebraic geometry the most basic and often considered case of descent theory is the descent of quasicoherent sheaves. However, SGA I also considers the descent of affine schemes over a base scheme.
The basic theorem is that the fibered category of affine morphisms over the site of base schemes with fpqc topology is a Grothendieck 1-stack (i.e. every fpqc morphism is of effective -descent).
This theorem uses more specific reasoning than the theory of descent for quasicoherent sheaves and unlike the former, it does not generalize to the noncommutative case.