Aims: We exploit deep observations of the GOODS-N field taken with PACS, the Photodetector Array Camera and Spectrometer, onboard of Herschel, as part of the PACS evolutionary probe guaranteed time (PEP), to study the link between star formation and stellar mass in galaxies to z ~ 2. Methods: Starting from a stellar mass - selected sample of ~4500 galaxies with mag4.5 µm < 23.0 (AB), we identify ~350 objects with a PACS detection at 100 or 160 μm and ~1500 with only Spitzer 24 μm counterpart. Stellar masses and total IR luminosities (LIR) are estimated by fitting the spectral energy distributions (SEDs). Results: Consistently with other Herschel results, we find that LIR based only on 24 μm data is overestimated by a median factor ~1.8 at z ~ 2, whereas it is underestimated (with our approach) up to a factor ~1.6 at 0.5 < z < 1.0. We then exploit this calibration to correct LIR based on the MIPS/Spitzer fluxes. These results clearly show how Herschel is fundamental to constrain LIR, and hence the star formation rate (SFR), of high redshift galaxies. Using the galaxies detected with PACS (and/or MIPS), we investigate the existence and evolution of the relations between the SFR, the specific star formation rate (SSFR=SFR/mass) and the stellar mass. Moreover, in order to avoid selection effects, we also repeat this study through a stacking analysis on the PACS images to fully exploit the far-IR information also for the Herschel and Spitzer undetected subsamples. We find that the SSFR-mass relation steepens with redshift, being almost flat at z < 1.0 and reaching a slope of α = -0.50+0.13-0.16 at z ~ 2, at odds with recent works based on radio-stacking analysis at the same redshift. The mean SSFR of galaxies increases with redshift, by a factor ~15 for massive M > 1011 M&sun; galaxies from z = 0 to z = 2, and seems to flatten at z > 1.5 in this mass range. Moreover, the most massive galaxies have the lowest SSFR at any z, implying that they have formed their stars earlier and more rapidly than their low mass counterparts (downsizing). Herschel is an ESA space observatory with science instruments provided by European-led Principal Investigator consortia and with important participation from NASA.Appendices are only available in electronic form at http://www.aanda.org