Context. The Vista Variables in the Vía Láctea (VVV) ESO Public Survey is a variability survey of the Milky Way bulge and an adjacent section of the disk carried out from 2010 on ESO Visible and Infrared Survey Telescope for Astronomy (VISTA). The VVV survey will eventually deliver a deep near-IR atlas with photometry and positions in five passbands (ZYJHKS) and a catalogue of 1-10 million variable point sources - mostly unknown - that require classifications. Aims: The main goal of the VVV Templates Project, which we introduce in this work, is to develop and test the machine-learning algorithms for the automated classification of the VVV light-curves. As VVV is the first massive, multi-epoch survey of stellar variability in the near-IR, the template light-curves that are required for training the classification algorithms are not available. In the first paper of the series we describe the construction of this comprehensive database of infrared stellar variability. Methods: First, we performed a systematic search in the literature and public data archives; second, we coordinated a worldwide observational campaign; and third, we exploited the VVV variability database itself on (optically) well-known stars to gather high-quality infrared light-curves of several hundreds of variable stars. Results: We have now collected a significant (and still increasing) number of infrared template light-curves. This database will be used as a training-set for the machine-learning algorithms that will automatically classify the light-curves produced by VVV. The results of such an automated classification will be covered in forthcoming papers of the series.