Traditionally Public Transport (PT) demand estimation relies on manual survey-based or, where available, smartcard passenger data. However, transport service providers and authorities make it rarely available to researchers. An additional challenge is the variety of formats and the low granularity in which such data is available. Recently, first steps towards the use of advanced ICT-based data-driven approaches have started to emerge. These new data sources can provide new opportunities for generating more data and insights into transit demand patterns and behaviour. In this paper, we propose a novel data-driven transit demand estimation process, TransitCrowd, and apply it to subway stations. Tran-sitCrowd estimates the passengers entering and exiting each station using as proxy the subway crowdness provided by Google Popular Times (GPT) crowdsensed information often available at sheer scale in any city. TransitCrowd's key component is its one-time calibration process, which creates temporal signatures of the stations based on historical GPT information, and regression-based machine learning and live GPT to predict passenger flows. We assess TransitCrowd's estimation accuracy for two cities across a two-months period, i.e., New York and Washington., showing very promising results for both estimation and real-time prediction of transit flows at subway stations.