We use N-body simulations and observationally-normalized relations between dark matter halo mass, stellar mass, and cold gas mass to derive robust, arguably inevitable expectations about the baryonic content of major mergers out to redshift z~2. First, we find that the majority of major mergers (m/M > 0.3) experienced by Milky Way size dark matter halos should have been gas-rich, and that gas-rich mergers are increasingly common at high redshift. Though the frequency of major mergers into galaxy halos in our simulations greatly exceeds the observed late-type galaxy fraction, the frequency of gas-poor major mergers is consistent with the observed fraction of spheroid-dominated galaxies across the halo mass range M_DM ~ 10^11-10^13 Msun. These results lend support to the conjecture that mergers with high baryonic gas fractions play an important role in building and/or preserving disk galaxies in the universe. Also, we find that the overall fraction of a galaxy's cold baryons deposited directly via major mergers is substantial. Approximately ~30% of the cold baryonic material in M_star ~ 10^10 Msun$ (M_DM ~ 10^11.5 Msun) galaxies is accreted as cold gas in major mergers. For more massive galaxies with M_star ~ 10^11 Msun (M_DM ~ 10^13 Msun) the fraction of baryons amassed in mergers is even higher, ~50%, but most of these accreted baryons are delivered directly in the form of stars. This baryonic mass deposition is almost unavoidable, and provides a limit on the fraction of a galaxy's cold baryons that can originate in cold flows or from hot halo cooling. Show Partial Abstract