We employ a high-resolution LCDM N-body simulation to present merger rate predictions for dark matter halos and investigate how common merger-related observables for galaxies--such as close pair counts, starburst counts, and the morphologically disturbed fraction--likely scale with luminosity, stellar mass, merger mass ratio, and redshift from z=0 to z=4. We provide a simple 'universal' fitting formula that describes our derived merger rates for dark matter halos a function of dark halo mass, merger mass ratio, and redshift, and go on to predict galaxy merger rates using number density-matching to associate halos with galaxies. For example, we find that the instantaneous merger rate of m/M>0.3 mass ratio events into typical L > f L* galaxies follows the simple relation dN/dt=0.03(1+f)(1+z)^2.1 Gyr^-1. Despite the rapid increase in merger rate with redshift, only a small fraction of >0.4 L* high-redshift galaxies (~3% at z=2) should have experienced a major merger (m/M >0.3) in the very recent past (t< 100 Myr). This suggests that short-lived, merger-induced bursts of star formation should not contribute significantly to the global star formation rate at early times, in agreement with observational indications. We emphasize that great care must be made in comparisons to observations because the predicted observables depend very sensitively on galaxy luminosity, redshift, overall mass ratio, and uncertain relaxation timescales for merger remnants. We show that the majority of bright galaxies at z=3 should have undergone a major merger (>0.3) in the last 700 Myr and conclude that mergers almost certainly play an important role in delivering baryons and influencing the kinematic properties of Lyman Break Galaxies (LBGs). Show Partial Abstract