The generic smooth cubic surface has 27 lines on it (working in $\Bbb CP^3$). However, it is not a ruled surface. On the other hand, a nonsingular quadric (working over $\Bbb R$ we need a saddle surface or a hyperboloid of one sheet) has two infinite families of pairwise skew lines on it. So I'm not quite sure what the result you're remembering might be.
Now, if you talk about smooth (real analytic) flat ruled surfaces in $\Bbb R^3$, they must be either planes, cones, cylinders, or tangent developables. Cylinders are ruled by parallel lines, but cones and tangent developables have infinitely many non-parallel rulings.