Disks around T Tauri stars are known to lose mass, as best shown by the profiles of the forbidden emission lines of low-ionization species. At least two separate kinematic components have been identified, one characterized by velocity shifts of tens to hundreds of km s super(-1) (HVC) and one with a much lower velocity of a few km s super(-1) (LVC). The HVC are convincingly associated to the emission of jets, but the origin of the LVC is still unknown. In this paper we analyze the forbidden line spectrum of a sample of 44 mostly low-mass young stars in Lupus and sigma Ori observed with the X-shooter ESO spectrometer. We detect forbidden line emission of OI, OII, S II, N I, and N II, and characterize the line profiles as LVC, blueshifted HVC, and redshifted HVC. We focus our study on the LVC. We show that there is a good correlation between line luminosity and both L sub(star) and the accretion luminosity (or the mass accretion rate) over a large interval of values (L sub(star) ~ 10 super(-2)-1 L sub(middot in circle); L sub(acc) ~ 10 super(-5)-10 super(-1) L sub(middot in circle); M sub(acc) ~ 10 super(-11)-10 super(-7) M sub(middot in circle)/yr). The lines show the presence of a slow wind (V sub(peak) < 20 km s super(-1)) that is dense (n sub(H) > 10 super(8) cm super(-3) ), warm (T ~ 5000-10 000 K), mostly neutral. We estimate the mass of the emitting gas and provide a value for the maximum volume it occupies. Both quantities increase steeply with the stellar mass, from ~10 super(-12) M sub(middot in circle) and ~0.01 AU super(3) for M sub(star) ~ 0.1 M sub(middot in circle), to ~3 x 10 super(-10) M sub(middot in circle) and ~1 AU super(3) for M sub(star) ~ 1 M sub(middot in circle), respectively. These results provide quite stringent constraints to wind models in low-mass young stars, that need to be explored further.