Conventional beamforming with fixed-orientation antenna (FOA) arrays may struggle to effectively enhance signal and/or suppress interference due to significant variations in antenna directive gains over different steering angles. To break this limitation, we investigate in this paper the rotatable antenna (RA)-enhanced single/multi-beam forming by exploiting the new spatial degrees of freedom (DoFs) via antennas' rotation optimization. Specifically, the antenna rotation angle vector (ARAV) and antenna weight vector (AWV) are jointly optimized to maximize the minimum array gain over signal directions, subject to a given constraint on the maximum array gain over interference directions. For the special case of single-beam forming without interference, the optimal ARAV is derived in closed-form with the maximum ratio combining (MRC) beamformer applied to the AWV. For the general case of multi-beam forming, we propose an efficient alternating optimization (AO) algorithm to find a high-quality suboptimal solution by iteratively optimizing one of the ARAV and AWV with the other being fixed. Simulation results demonstrate that the proposed RA-based scheme can significantly outperform the traditional FOA-based and isotropic antenna (IA)-based schemes in terms of array gain.