We investigate the effects of the long-range dipolar interaction on the formation of the stripe patterns in two-dimensional (2D) spin systems with competing short- and long-range interactions by using the continuous time Monte Carlo technique. We find that there exists an optimal temperature region at which the best stripe patterns are prone to be formed, and the stability and the orientational ordering of striped structures mainly depend on the temperature T, while the width of the striped domains is determined by the strength of the long-range dipolar interaction g. Furthermore, a complete T-g phase diagram is obtained. The results provide a simple and universal picture to account for striking and substantial physics revealed in the prevalent striped morphologies of 2D spin systems.