Free-space optical (FSO) communication systems are negatively affected by two physical phenomenon, namely, scintillation due to atmospheric turbulence and pointing errors. To quantify the effect of these two factors on FSO system performance, we need an effective mathematical model for them. In this paper, we propose and study a generalized pointing error model based on the Beckmann distribution. We then derive a generic expression of the asymptotic capacity of FSO systems under the joint impact of turbulence and generalized pointing error impairments. Finally, the asymptotic channel capacity formula are extended to quantify the FSO systems performance with selection and switched-and-stay diversity.