Context. The volume of data generated by astronomical surveys is growing rapidly. Traditional analysis techniques in spectroscopy either demand intensive human interaction or are computationally expensive. In this scenario, machine learning, and unsupervised clustering algorithms in particular, offer interesting alternatives. The Apache Point Observatory Galactic Evolution Experiment (APOGEE) offers a vast data set of near-infrared stellar spectra, which is perfect for testing such alternatives. Aims: Our research applies an unsupervised classification scheme based on K-means to the massive APOGEE data set. We explore whether the data are amenable to classification into discrete classes. Methods: We apply the K-means algorithm to 153 847 high resolution spectra (R ≈ 22 500). We discuss the main virtues and weaknesses of the algorithm, as well as our choice of parameters. Results: We show that a classification based on normalised spectra captures the variations in stellar atmospheric parameters, chemical abundances, and rotational velocity, among other factors. The algorithm is able to separate the bulge and halo populations, and distinguish dwarfs, sub-giants, RC, and RGB stars. However, a discrete classification in flux space does not result in a neat organisation in the parameters' space. Furthermore, the lack of obvious groups in flux space causes the results to be fairly sensitive to the initialisation, and disrupts the efficiency of commonly-used methods to select the optimal number of clusters. Our classification is publicly available, including extensive online material associated with the APOGEE Data Release 12 (DR12). Conclusions: Our description of the APOGEE database can help greatly with the identification of specific types of targets for various applications. We find a lack of obvious groups in flux space, and identify limitations of the K-means algorithm in dealing with this kind of data. Full Tables B.1-B.4 are only available at the CDS via anonymous ftp to http://cdsarc.u-strasbg.fr (http://130.79.128.5) or via http://cdsarc.u-strasbg.fr/viz-bin/qcat?J/A+A/612/A98