Image-to-image translation is considered a next frontier in the field of medical image analysis, with numerous potential applications. However, recent advances in this field offer individualized solutions by utilizing specialized architectures which are task specific or by suffering from limited capacities and thus requiring refinement through non end-to-end training. In this paper, we propose a novel general purpose framework for medical image-to-image translation, titled MedGAN, which operates in an end-to-end manner on the image level. MedGAN builds upon recent advances in the field of generative adversarial networks(GANs) by combining the adversarial framework with a unique combination of non-adversarial losses which captures the high and low frequency components of the desired target modality. Namely, we utilize a discriminator network as a trainable feature extractor which penalizes the discrepancy between the translated medical images and the desired modalities in the pixel and perceptual sense. Moreover, style-transfer losses are utilized to match the textures and fine-structures of the desired target images to the outputs. Additionally, we present a novel generator architecture, titled CasNet, which enhances the sharpness of the translated medical outputs through progressive refinement via encoder decoder pairs. To demonstrate the effectiveness of our approach, we apply MedGAN on three novel and challenging applications: PET-CT translation, correction of MR motion artefacts and PET image denoising. Qualitative and quantitative comparisons with state-of-the-art techniques have emphasized the superior performance of the proposed framework. MedGAN can be directly applied as a general framework for future medical translation tasks.