Cryptocurrency prices are highly volatile, making them a consistent target for machine learning models. This paper explores the application of advanced Recurrent Neural Networks (RNNs), specifically Long Short-Term Memory (LSTM) and Gated Recurrent Unit (GRU) networks, as well as traditional statistical and machine learning methods to predict the closing prices of major cryptocurrencies. Using daily price data sourced from public cryptocurrency exchange, the performance of RNN models with traditional predictive models was compared to determine the most effective approach. By evaluating model performance across cryptocurrencies with varying levels of volatility, it highlights how volatility influences predictive accuracy. Results indicate that both LSTM and GRU models outperform baseline statistical models with lower error rates. Additionally, traditional machine learning models, like decision trees and random forests, showed notable success with low-volatility assets, such as XRP, underscoring their suitability for stable data. These findings highlight the potential of deep learning techniques in capturing cryptocurrency market dynamics.