Accurate range prediction of an electric vehicle is an important open problem, affecting among others the adoption and market penetration of electric vehicles. Current range prediction systems suffer several practical limitations. Most critically these systems employ models in which all vehicle-specific parameters are required to be known. In this paper, we propose a methodology for predicting power and mission energy of electric vehicles that does not require knowledge of vehicle-specific parameters nor a drive-train model. The proposed method uses a data-driven approach grounded entirely on available vehicle sensor data. In particular, the predictive model is obtained by applying machine learning techniques, and in order to adapt to changing conditions in real-time, the specific class of kernel adaptive filtering algorithms is employed. Kernel adaptive filtering extends the theory of linear filters with concepts from kernel methods in order to construct nonlinear adaptive filtering algorithms that exhibit properties such as universal approximation capabilities and convexity in training, requiring only modest computational complexity. After providing an overview of the most relevant properties of kernel adaptive filters, we evaluate the proposed prediction methodology on data obtained in nine vehicle trial runs, comparing the performance of one linear adaptive filter, one online trained neural network and two state-of-the-art kernel adaptive filters.