In this paper, we experiment with the recently introduced subword regularization technique \cite{kudo2018subword} in the context of end-to-end automatic speech recognition (ASR). We present results from both attention-based and CTC-based ASR systems on two common benchmark datasets, the 80 hour Wall Street Journal corpus and 1,000 hour Librispeech corpus. We also introduce a novel subword beam search decoding algorithm that significantly improves the final performance of the CTC-based systems. Overall, we find that subword regularization improves the performance of both types of ASR systems, with the regularized attention-based model performing best overall.