We study the redshift evolution of galaxy pair fractions and merger rates for different types of galaxies using kinematic pairs selected from the DEEP2 Redshift Survey. By parameterizing the evolution of the pair fraction as (1+z)^{m}, we find that the companion rate increases mildly with redshift with m = 0.41+-0.20 for all galaxies with -21 < M_B^{e} < -19. Blue galaxies show slightly faster evolution in the blue companion rate with m = 1.27+-0.35 while red galaxies have had fewer red companions in the past as evidenced by the negative slope m = -0.92+-0.59. We find that at low redshift the pair fraction within the red sequence exceeds that of the blue cloud, indicating a higher merger probability among red galaxies compared to that among the blue galaxies. With further assumptions on the merger timescale and the fraction of pairs that will merge, the galaxy major merger rates for 0.1 < z <1.2 are estimated to be ~10^{-3}h^{3}Mpc^{-3}Gyr^{-1} with a factor of 2 uncertainty. At z ~ 1.1, 68% of mergers are wet, 8% of mergers are dry, and 24% of mergers are mixed, compared to 31% wet mergers, 25% dry mergers, and 44% mixed mergers at z ~ 0.1. The growth of dry merger rates with decreasing redshift is mainly due to the increase in the co-moving number density of red galaxies over time. About 22% to 54% of present-day L^{*} galaxies have experienced major mergers since z ~ 1.2, depending on the definition of major mergers. Moreover, 24% of the red galaxies at the present epoch have had dry mergers with luminosity ratios between 1:4 and 4:1 since z ~ 1. Our results also suggest that the wet mergers and/or mixed mergers may be partially responsible for producing red galaxies with intermediate masses while a significant portion of massive red galaxies is assembled through dry mergers at later times.
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