In this paper, we demonstrate the efficacy of transfer learning and continuous learning for various automatic speech recognition (ASR) tasks using end-to-end models trained with CTC loss. We start with a large pre-trained English ASR model and show that transfer learning can be effectively and easily performed on{:} (1) different English accents, (2) different languages (from English to German, Spanish, Russian, or from Mandarin to Cantonese) and (3) application-specific domains. Our extensive set of experiments demonstrate that in all three cases, transfer learning from a good base model has higher accuracy than a model trained from scratch. Our results indicate that, for fine-tuning, larger pre-trained models are better than small pre-trained models, even if the dataset for fine-tuning is small. We also show that transfer learning significantly speeds up convergence, which could result in significant cost savings when training with large datasets.