The correct answer is $\boxed{\text{B. }S-180^\circ}$.
The spherical excess of a spherical triangle is the sum of its three interior angles minus $180^\circ$. This is because the sum of the interior angles of a spherical triangle is always greater than $180^\circ$, due to the curvature of the sphere.
Option A is incorrect because the spherical excess is always less than $180^\circ$.
Option C is incorrect because the spherical excess is always greater than $-180^\circ$.
Option D is incorrect because the spherical excess is always less than $360^\circ$.