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 (UKIDSS) and the Two Micron All Sky Survey (2MASS) in the $K-$band ($sim 2.2~mu$m). Combined with all available spectroscopy, our $K-$band selected sample contains $sim 250,000$ 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 $sim 2%$ as a function of $K-$band luminosity for galaxies in the range $10^8 - 10^{12} L_{odot}$, 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 $sim 40-50%$ 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 ($m = 0.7 pm 0.1$), in the relation $f_{rm{pair}} propto (1+z)^m$, than indicated in many previous studies. These results indicate that a typical $Lsim L^*$ galaxy has undergone $sim 0.2-0.8$ major mergers since $z=1$ (depending on the assumptions of merger timescale and percentage of pairs that actually merge).
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