We present a study of the largest available sample of near-infrared selected (i.e., stellar mass selected) dynamically close pairs of galaxies at low redshifts (z < 0.3). We combine this sample with new estimates of the major merger pair fraction for stellar mass selected galaxies at z < 0.8, from the Red Sequence Cluster Survey (RCS1). We construct our low-redshift K-band selected sample using photometry from the UKIRT Infrared Deep Sky Survey and the Two Micron All Sky Survey (2MASS) in the K band (similar to 2.2 mu m). Combined with all available spectroscopy, our K-band selected sample contains similar to 250,000 galaxies and is > 90% spectroscopically complete. The depth and large volume of this sample allow us to investigate the low-redshift pair fraction and merger rate of galaxies over a wide range in K-band luminosity. We find the major merger pair fraction to be flat at similar to 2% as a function of K-band luminosity for galaxies in the range 10(8)-10(12) L-circle dot, in contrast to recent results from studies in the local group that find a substantially higher low-mass pair fraction. This low-redshift major merger pair fraction is similar to 40%-50% higher than previous estimates drawn from K-band samples, which were based on 2MASS photometry alone. Combining with the RCS1 sample, we find a much flatter evolution (m = 0.7 +/- 0.1) in the relation f(pair) alpha (1 + z) (m) than indicated in many previous studies. These results indicate that a typical L similar to L* galaxy has undergone similar to 0.2-0.8 major mergers since z = 1 (depending on the assumptions of merger timescale and percentage of pairs that actually merge).