In this paper we show that manifolds without conjugate points exhibit rigidity phenomena similar to that studied in [BGS, Section I.5]. The main theorem is that if $X$ is a complete, simply connected Riemannian manifold without conjugate points, and $M=X\times R$ is given the Riemannian product metric $g$, then any metric without conjugate points on $M$ which agrees with $g$ outside a compact set is isometric to $g$.