Using the k-means cluster analysis algorithm, we carry out an unsupervised classification of all galaxy spectra in the seventh and final Sloan Digital Sky Survey data release (SDSS/DR7). Except for the shift to rest-frame wavelengths and the normalization to the g-band flux, no manipulation is applied to the original spectra. The algorithm guarantees that galaxies with similar spectra belong to the same class. We find that 99% of the galaxies can be assigned to only 17 major classes, with 11 additional minor classes including the remaining 1%. The classification is not unique since many galaxies appear in between classes; however, our rendering of the algorithm overcomes this weakness with a tool to identify borderline galaxies. Each class is characterized by a template spectrum, which is the average of all the spectra of the galaxies in the class. These low-noise template spectra vary smoothly and continuously along a sequence labeled from 0 to 27, from the reddest class to the bluest class. Our Automatic Spectroscopic K-means-based (ASK) classification separates galaxies in colors, with classes characteristic of the red sequence, the blue cloud, as well as the green valley. When red sequence galaxies and green valley galaxies present emission lines, they are characteristic of active galactic nucleus activity. Blue galaxy classes have emission lines corresponding to star formation regions. We find the expected correlation between spectroscopic class and Hubble type, but this relationship exhibits a high intrinsic scatter. Several potential uses of the ASK classification are identified and sketched, including fast determination of physical properties by interpolation, classes as templates in redshift determinations, and target selection in follow-up works (we find classes of Seyfert galaxies, green valley galaxies, as well as a significant number of outliers). The ASK classification is publicly accessible through various Web sites.