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In this paper the performance of different Machine Learning and Deep Learning approaches is evaluated in problems related to green mobility in big cities. Specifically, the forecasting of bike sharing demand in Madrid and Barcelona (Spain) is approached, for different prediction time-horizons, and also a problem of cable car demand forecasting in Madrid city. An important number of predictive variables are considered, which are grouped into four different sets (categorical/calendrical, persistence-based, meteorological and, as a novelty of the paper, information about analogue past instances), whose relevance is studied for all cases. A feature selection mechanism is also incorporated in order to improve the prediction accuracy of the proposed algorithms. A total of 12 different multivariate regression techniques are implemented, covering from Machine Learning methods to time-series Deep Learning approaches. Excellent results in all the prediction problems approached are reported. Finally, the consequences of obtaining accurate prediction in these three problem of green mobility in big cities are discussed. In addition, it is studied how the results could be exported to other similar cases in more general urban mobility studies. Novelties of the work include: (1) Addressing the forecast problem of passenger flow on a cable car using ML and DL multivariate techniques; (2) using the demand of analogous past instances as an additional feature to solve the demand prediction problems; and (3) the extraction of global conclusions about feature relevance when addressing a demand forecasting problem in green mobility. [ABSTRACT FROM AUTHOR]