Stokes profiles emerging from the magnetized quiet photosphere and observed by the Solar Optical Telescope (SOT) spectropolarimeter (SP) aboard the Hinode satellite present a large variety of complex shapes. These are indicative of unresolved magnetic structures and/or gradients along the line of sight that have been overlooked in the inversion analyses performed so far. The interpretation of the complex shapes of SOT/SP Stokes V profiles for the understanding of the quiet Sun magnetism must be seriously considered in the near future. In fact, Stokes V profiles significantly deviating from an antisymmetric shape are rather common in the quiet Sun and, in particular, in intranetwork (IN) regions. Here we present the results of the analysis of the shapes of SOT/SP Stokes V profiles performed through a k-means classification. Such an analysis aims at defining different profile classes representative of SOT/SP polarization measurements. We found that about 35 classes can be defined from quiet Sun measurements. Among these, two main subsets can be recognized: network profiles and IN profiles. Approximately 34% of quiet Sun profiles present important asymmetries. From such results, it follows that new inversion techniques able to reproduce line asymmetries must be considered in future analyses of Hinode SOT/SP measurements. The number of line shapes to be reproduced by such analyses is finite and small.