Bitcoin has recently received a lot of attention from the media and the public due to its recent price surge and crash. Correspondingly, many researchers have investigated various factors that affect the Bitcoin price and the patterns behind its fluctuations, in particular, using various machine learning methods. In this paper, we study and compare various state-of-the-art deep learning methods such as a deep neural network (DNN), a long short-term memory (LSTM) model, a convolutional neural network, a deep residual network, and their combinations for Bitcoin price prediction. Experimental results showed that although LSTM-based prediction models slightly outperformed the other prediction models for Bitcoin price prediction (regression), DNN-based models performed the best for price ups and downs prediction (classification). In addition, a simple profitability analysis showed that classification models were more effective than regression models for algorithmic trading. Overall, the performances of the proposed deep learning-based prediction models were comparable.