Accurate hydrological predictions are required to prepare for the impacts of climate change, especially in India, which experiences frequent floods and droughts. However, the complex hydrological processes of its distinct watersheds and limited data make it challenging to deliver highly-performant hydrologic predictions using conventional models. Moreover, it remains uncertain where the limits of predictability are and whether recently-popular deep learning approaches can offer significant improvements. Here, we tested the first instance of the hydrologic model based on long short-term memory (LSTM) for 55 Indian watersheds, using a new dataset comprising forcing, attributes, and discharge data. Our results show that the LSTM model provides much-improved performance compared to conventional models in India, providing a median Nash-Sutcliffe efficiency (NSE) of 0.56. The LSTM model trained on all the watersheds is more favourable to those trained on individual or homogeneous watersheds, as it benefits from a broader range of hydrological processes and patterns in the input data. However, the LSTM model performs poorly for non-perennial, large, and semi-arid climate zone watersheds due to its inability to simulate the complex hydrological processes specific to these environments. Integrating lagged observations with the LSTM model (referred to as DI-LSTM) improved the predictions in such watersheds and enhanced the median NSE to 0.76 by capturing the temporal dependencies and historical patterns that influence hydrological processes. Overall, the contrast of model performance across watersheds suggests major limitations could be associated with the quality of forcing data, and the slow flow or groundwater processes are highly important in the Indian subcontinent. Notably, both LSTM and DI-LSTM models performed reasonably well for predictions in ungauged watersheds. The findings of this study demonstrate that data-sparse countries, too, can benefit from big-data deep learning and point out further avenues toward model improvements.