Water at interfaces governs many processes on the molecular scale from electrochemical and enzymatic reactions to protein folding. Here we focus on water transport through proteinaceous pores that are so narrow that the water molecules cannot overtake each other in the pore. After a short introduction into the single-file transport theory, we analyze experiments in which the unitary water permeability, p_f, of water channel proteins (aquaporins, AQPs), potassium channels (KcsA), and antibiotics (gramicidin-A derivatives) has been obtained. A short outline of the underlying methods (scanning electrochemical microscopy, fluorescence correlation spectroscopy, measurements of vesicle light scattering) is also provided. We conclude that p_f increases exponentially with a decreasing number N_H of hydrogen bond donating or accepting residues in the channel wall. The variance in N_H is responsible for a more than hundredfold change in p_f. The dehydration penalty at the channel mouth has a smaller effect on p_f. The intricate link between p_f and the Gibbs activation energy barrier, ΔG^‡_t, for water flow suggests that conformational transitions of water channels act as a third determinant of p_f.