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Multi-cell cooperation is an effective means to improve service quality to cellular users. Existing work primarily focuses on interference cancellation using all the degrees of freedom (DoF). This leads to low service quality for some users with poor channel quality to its serving base station. This work investigates the multi-cell beamforming design for simultaneously enhancing the downlink signal strength and mitigating interference. We first consider the ideal case when perfect channel state information (CSI) is available for determining the beamforming vectors and then extend to the case of imperfect CSI. For both cases, the beamforming optimization problems are non-convex. Assuming perfect CSI, we obtain the optimal joint transmit (JT) beamforming vectors based on the uplink-downlink duality. In the presence of unknown CSI errors, we use the semidefinite relaxation (SDR) with Bernstein-type inequality to derive the robust JT beamforming. Numerical results are presented to evaluate the performance of the proposed schemes.