Classical examples of two-dimensional saddle surfaces in the Euclidean space are second order surfaces, the hyperbolic paraboloid z=x^2-y^2 (which is often referred to as "the saddle surface" or "the standard saddle surface") and the hyperboloid of one sheet.
Saddle surfaces have negative Gaussian curvature which distinguish them from convex/elliptical surfaces which have positive Gaussian curvature.