Lack of ground-truth MR images impedes the common supervised training of neural networks for image reconstruction. To cope with this challenge, this article leverages unpaired adversarial training for reconstruction networks, where the inputs are undersampled k-space and naively reconstructed images from one dataset, and the labels are high-quality images from another dataset. The reconstruction networks consist of a generator which suppresses the input image artifacts, and a discriminator using a pool of (unpaired) labels to adjust the reconstruction quality. The generator is an unrolled neural network - a cascade of convolutional and data consistency layers. The discriminator is also a multilayer CNN that plays the role of a critic scoring the quality of reconstructed images based on the Wasserstein distance. Our experiments with knee MRI datasets demonstrate that the proposed unpaired training enables diagnostic-quality reconstruction when high-quality image labels are not available for the input types of interest, or when the amount of labels is small. In addition, our adversarial training scheme can achieve better image quality (as rated by expert radiologists) compared with the paired training schemes with pixel-wise loss.