Combining data from varied sources has considerable potential for knowledge discovery: collaborating data parties can mine data in an expanded feature space, allowing them to explore a larger range of scientific questions. However, data sharing among different parties is highly restricted by legal conditions, ethical concerns, and / or data volume. Fueled by these concerns, the fields of cryptography and distributed learning have made great progress towards privacy-preserving and distributed data mining. However, practical implementations have been hampered by the limited scope or computational complexity of these methods. In this paper, we greatly extend the range of analyses available for vertically partitioned data, i.e., data collected by separate parties with different features on the same subjects. To this end, we present a novel approach for privacy-preserving generalized linear models, a fundamental and powerful framework underlying many prediction and classification procedures. We base our method on a distributed block coordinate descent algorithm to obtain parameter estimates, and we develop an extension to compute accurate standard errors without additional communication cost. We critically evaluate the information transfer for semi-honest collaborators and show that our protocol is secure against data reconstruction. Through both simulated and real-world examples we illustrate the functionality of our proposed algorithm. Without leaking information, our method performs as well on vertically partitioned data as existing methods on combined data -- all within mere minutes of computation time. We conclude that our method is a viable approach for vertically partitioned data analysis with a wide range of real-world applications.