We have obtained 1087 NIR (JHK_s_) measurements of 21 SNe Ia using PAIRITEL, nearly doubling the number of well-sampled NIR SN Ia light curves. These data strengthen the evidence that SNe Ia are excellent standard candles in the NIR, even without correction for optical light-curve shape. We construct fiducial NIR templates for normal SNe Ia from our sample, excluding only the three known peculiar SNe Ia: SN 2005bl, SN 2005hk, and SN 2005ke. The H-band absolute magnitudes in this sample of 18 SNe Ia have an intrinsic rms of only 0.15mag with no correction for light-curve shape. We found a relationship between the H-band extinction and optical color excess of A_H_=0.2E(B-V). This variation is as small as the scatter in distance modulus measurements currently used for cosmology based on optical light curves after corrections for light-curve shape. Combining the homogeneous PAIRITEL measurements with 23 SNe Ia from the literature, these 41 SNe Ia have standard H-band magnitudes with an rms scatter of 0.16mag. The good match of our sample with the literature sample suggests there are few systematic problems with the photometry.