We investigate the near-infrared K-band properties of the brightest cluster galaxies (BCGs) in a sample of 93 galaxy clusters and groups, using data from the Two Micron All Sky Survey. Our cluster sample spans a factor of 70 in mass, making it sensitive to cluster mass related trends. We study the correlations between the BCG luminosity L_b and the mass or luminosity of the host clusters, finding that BCGs in more massive clusters are more luminous than their counterparts in less massive systems, and that the BCGs become less important in the overall cluster light L200 as cluster mass increases. We argue that BCGs grow in luminosity mainly by merging with other luminous galaxies as the host clusters grow hierarchically; the decreasing BCG luminosity fraction L_b/L_200 with cluster mass indicates that the rate of luminosity growth in BCGs is slow compared to the rate at which clusters acquire galaxy light from the field or other merging clusters. We use the observed cluster luminosity-mass relation and a merger tree model to estimate that the amount of intracluster light (ICL) increases with cluster mass; calculations suggest that in 10^{15}Mo clusters more than 50% of total stellar mass is in ICL. The cluster baryon fraction accounting for the ICL is in good agreement with the CMB constraints. The inclusion of ICL reduces thediscrepancy between the observed cluster cold baryon fraction and that found in hydro simulations. Based on the observed Fe abundance in the ICM, we find that the predicted ICL together with the observed galaxy light, match the Fe mass-tolight ratio expected from simple stellar population models with a Salpeter IMF. The ICL also makes it easier to produce the Fe core excess found in cool-core clusters. (abridged)

18 pages, 9 figures, accepted for publication in the Astrophysical Journal