We aim to perform a statistical study of stellar flares observed by Kepler. We want to study the flare amplitude, duration, energy, and occurrence rates, and how they are related to the spectral type and rotation period. To that end, we have developed an automated flare detection and characterization algorithm. We have harvested the stellar parameters from the Kepler input catalog and the rotation periods from McQuillan et al. (2014, Cat. J/ApJS/211/24). We find several new candidate A stars showing flaring activity. Moreover, we find 653 giants with flares. From the statistical distribution of flare properties, we find that the flare amplitude distribution has a similar behavior between F+G types and K+M types. The flare duration and flare energy seem to be grouped between G+K+M types versus F types and giants. We also detect a tail of stars with high flare occurrence rates across all spectral types (but most prominent in the late spectral types), and this is compatible with the existence of "flare stars." Finally, we have found a strong correlation of the flare occurrence rate and the flare amplitude with the stellar rotation period: a quickly rotating star is more likely to flare often and has a higher chance of generating large flares.